38
WSSV - White spot syndrome virus RCN Marine Disease Modeling and Transmission Workshop – May 2015

WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

  • Upload
    others

  • View
    2

  • Download
    0

Embed Size (px)

Citation preview

Page 1: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

WSSV - White spot syndrome virus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Digestive tract Ventral Nerve chord

Circulatory system Respiratory system

Hematopoietic tissueLymphoid organ

Female reproductive tract Male reproductive tract

Decapod anatomy

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

210-380nm

70-167nm

Envelope

Envelope proteins

Envelope extension

Nucleocapsid

Genome

Tegument

bull dsDNA - ~300kbpbull 185 ORFs

bull Baculoviralesbull Nimaviridae

bull Whispovirus

WSSV

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

ldquoBaculoviralesrdquoNimaviruses

HystrosavirusesGpSGHV

MdGHV

WSSV

CunNPV

NeleNPV

AcMNPV

CpGV

HzNV-1

PmNV

GbNV

OrNV

CcBV

TnZBV

CiBV

Bracoviruses

Nudiviruses

Baculoviruses

Wang Y Jehle JA 2009 JIP 101 187-193 Wang Y et al 2011 Vir Gen 42444 ndash 456 Theacutezeacute J et al 2011 PNAS 10815931-35

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Source FAO

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

1950 1970 1990 2010

75

25

Poun

ds (x

109 )

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Shrimp commodity production

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Shrimp Aquaculture SpeciesLitopenaeus vannamei Penaeus monodon

Marsupenaeus japonicusFenneropenaeus chinensis

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

050

100150200250300350400450500

1980 1985 1990 1995

Year

Mill

ions

of P

ound

s

Production of Farmed Shrimp - China

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

19921994 1994 1998

1996

19932002

200219971995

1999

19991999

1999

2005

Spread of WSSV

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Emergence of White spot syndrome virus

1 km

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 Environment changes bringing new contactsMore shrimpPonds built in new areas ndash where shrimp never were or in low numbersMore contact between other (terrestrial) arthropods and shrimp

2 Change in pathogen virulence

3 Introduced from elsewhere

Emergence of White spot syndrome virus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Source FAO

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Hosts of WSSV bull Shrimp

ndash Penaeusbull monodonbull semisulcatus

ndash Farfantepenaeusbull aztecusbull duorarum

ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus

ndash Marsupenaeusbull japonicus

ndash Litopenaeusbull vannameibull stylirostrisbull setiferus

ndash Metapenaeus ensis

ndash Exopalaemonbull orientalis

ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio

bull Crabndash Calappa lophosndash Charybdis

bull feriatabull natotor

ndash Helice spndash Portunus

bull pelagicusbull Sanguineolentus

ndash Callinectes sapidus

ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina

bull Lobsterndash Panuluris

bull longipesbull ornatusbull argus

bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

0

100

200

300

400

500

600

700

800

900

1000

0 3 6 9 12 15 18 21

Num

ber o

f shr

imp

Day

Weight 3 gDensity 550m3

Dose 003 bwfinal survival 000 003max daily mortality 10 06

WSSV Litopenaeus vannamei

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Armasus cinereum

Uca panacea

Callinectes sapidus

Litopenaeus setiferus

Uca speciosa

Local decapods exposed to WSSV (China)

0 5 10 15 20 25 30Day

00

01

02

03

04

05

06

07

08

09

10

Surv

ival

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Salt marshes

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Mississippi sound

Jourdan

Biloxi

Pearl

Wolf

Lake Pontchartrain

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Prevalence of WSSV in decapods of Ms Sound

Blue crab (Callinectes sapidus) (83 n=12)

Purple marsh crab (Sesarma reticulatum) (100 n=20)

Gulf mud fiddler crab (Uca longisignalis) (500 n=72)

Panacea sand fiddler crab (U panacea) (108 n=1404)

Mudflat fiddler crab (U rapax) (230 n=88)

Spined fiddler crab (U spinicarpa) (357 n=98)

Red-jointed fiddler crab (U minax) (227 n=22)

Squareback marsh crab (Armasus cinereum) (267 n=30)

Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)

White shrimp (Litopenaeus setiferus) (200 n=40)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Modeling WSSV in communities of decapods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram

λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass

δ η

Susceptible Infected Dead

β

χ

λ

micro

α micro

( ) ( )( )( ) ( )( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( )

1

1

1

1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ λ micro

β χ α micro

α micro η δ

+

+

+

= minus sdot minus minus minus + minus

= + sdot minus minus minus minus minus minus sdot minus sdot

= + minus minus sdot minus sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

Transmission terms - Force of infection λprobability of infection after contact

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 2: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

Digestive tract Ventral Nerve chord

Circulatory system Respiratory system

Hematopoietic tissueLymphoid organ

Female reproductive tract Male reproductive tract

Decapod anatomy

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

210-380nm

70-167nm

Envelope

Envelope proteins

Envelope extension

Nucleocapsid

Genome

Tegument

bull dsDNA - ~300kbpbull 185 ORFs

bull Baculoviralesbull Nimaviridae

bull Whispovirus

WSSV

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

ldquoBaculoviralesrdquoNimaviruses

HystrosavirusesGpSGHV

MdGHV

WSSV

CunNPV

NeleNPV

AcMNPV

CpGV

HzNV-1

PmNV

GbNV

OrNV

CcBV

TnZBV

CiBV

Bracoviruses

Nudiviruses

Baculoviruses

Wang Y Jehle JA 2009 JIP 101 187-193 Wang Y et al 2011 Vir Gen 42444 ndash 456 Theacutezeacute J et al 2011 PNAS 10815931-35

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Source FAO

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

1950 1970 1990 2010

75

25

Poun

ds (x

109 )

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Shrimp commodity production

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Shrimp Aquaculture SpeciesLitopenaeus vannamei Penaeus monodon

Marsupenaeus japonicusFenneropenaeus chinensis

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

050

100150200250300350400450500

1980 1985 1990 1995

Year

Mill

ions

of P

ound

s

Production of Farmed Shrimp - China

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

19921994 1994 1998

1996

19932002

200219971995

1999

19991999

1999

2005

Spread of WSSV

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Emergence of White spot syndrome virus

1 km

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 Environment changes bringing new contactsMore shrimpPonds built in new areas ndash where shrimp never were or in low numbersMore contact between other (terrestrial) arthropods and shrimp

2 Change in pathogen virulence

3 Introduced from elsewhere

Emergence of White spot syndrome virus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Source FAO

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Hosts of WSSV bull Shrimp

ndash Penaeusbull monodonbull semisulcatus

ndash Farfantepenaeusbull aztecusbull duorarum

ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus

ndash Marsupenaeusbull japonicus

ndash Litopenaeusbull vannameibull stylirostrisbull setiferus

ndash Metapenaeus ensis

ndash Exopalaemonbull orientalis

ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio

bull Crabndash Calappa lophosndash Charybdis

bull feriatabull natotor

ndash Helice spndash Portunus

bull pelagicusbull Sanguineolentus

ndash Callinectes sapidus

ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina

bull Lobsterndash Panuluris

bull longipesbull ornatusbull argus

bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

0

100

200

300

400

500

600

700

800

900

1000

0 3 6 9 12 15 18 21

Num

ber o

f shr

imp

Day

Weight 3 gDensity 550m3

Dose 003 bwfinal survival 000 003max daily mortality 10 06

WSSV Litopenaeus vannamei

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Armasus cinereum

Uca panacea

Callinectes sapidus

Litopenaeus setiferus

Uca speciosa

Local decapods exposed to WSSV (China)

0 5 10 15 20 25 30Day

00

01

02

03

04

05

06

07

08

09

10

Surv

ival

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Salt marshes

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Mississippi sound

Jourdan

Biloxi

Pearl

Wolf

Lake Pontchartrain

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Prevalence of WSSV in decapods of Ms Sound

Blue crab (Callinectes sapidus) (83 n=12)

Purple marsh crab (Sesarma reticulatum) (100 n=20)

Gulf mud fiddler crab (Uca longisignalis) (500 n=72)

Panacea sand fiddler crab (U panacea) (108 n=1404)

Mudflat fiddler crab (U rapax) (230 n=88)

Spined fiddler crab (U spinicarpa) (357 n=98)

Red-jointed fiddler crab (U minax) (227 n=22)

Squareback marsh crab (Armasus cinereum) (267 n=30)

Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)

White shrimp (Litopenaeus setiferus) (200 n=40)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Modeling WSSV in communities of decapods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram

λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass

δ η

Susceptible Infected Dead

β

χ

λ

micro

α micro

( ) ( )( )( ) ( )( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( )

1

1

1

1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ λ micro

β χ α micro

α micro η δ

+

+

+

= minus sdot minus minus minus + minus

= + sdot minus minus minus minus minus minus sdot minus sdot

= + minus minus sdot minus sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

Transmission terms - Force of infection λprobability of infection after contact

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 3: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

210-380nm

70-167nm

Envelope

Envelope proteins

Envelope extension

Nucleocapsid

Genome

Tegument

bull dsDNA - ~300kbpbull 185 ORFs

bull Baculoviralesbull Nimaviridae

bull Whispovirus

WSSV

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

ldquoBaculoviralesrdquoNimaviruses

HystrosavirusesGpSGHV

MdGHV

WSSV

CunNPV

NeleNPV

AcMNPV

CpGV

HzNV-1

PmNV

GbNV

OrNV

CcBV

TnZBV

CiBV

Bracoviruses

Nudiviruses

Baculoviruses

Wang Y Jehle JA 2009 JIP 101 187-193 Wang Y et al 2011 Vir Gen 42444 ndash 456 Theacutezeacute J et al 2011 PNAS 10815931-35

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Source FAO

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

1950 1970 1990 2010

75

25

Poun

ds (x

109 )

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Shrimp commodity production

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Shrimp Aquaculture SpeciesLitopenaeus vannamei Penaeus monodon

Marsupenaeus japonicusFenneropenaeus chinensis

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

050

100150200250300350400450500

1980 1985 1990 1995

Year

Mill

ions

of P

ound

s

Production of Farmed Shrimp - China

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

19921994 1994 1998

1996

19932002

200219971995

1999

19991999

1999

2005

Spread of WSSV

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Emergence of White spot syndrome virus

1 km

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 Environment changes bringing new contactsMore shrimpPonds built in new areas ndash where shrimp never were or in low numbersMore contact between other (terrestrial) arthropods and shrimp

2 Change in pathogen virulence

3 Introduced from elsewhere

Emergence of White spot syndrome virus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Source FAO

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Hosts of WSSV bull Shrimp

ndash Penaeusbull monodonbull semisulcatus

ndash Farfantepenaeusbull aztecusbull duorarum

ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus

ndash Marsupenaeusbull japonicus

ndash Litopenaeusbull vannameibull stylirostrisbull setiferus

ndash Metapenaeus ensis

ndash Exopalaemonbull orientalis

ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio

bull Crabndash Calappa lophosndash Charybdis

bull feriatabull natotor

ndash Helice spndash Portunus

bull pelagicusbull Sanguineolentus

ndash Callinectes sapidus

ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina

bull Lobsterndash Panuluris

bull longipesbull ornatusbull argus

bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

0

100

200

300

400

500

600

700

800

900

1000

0 3 6 9 12 15 18 21

Num

ber o

f shr

imp

Day

Weight 3 gDensity 550m3

Dose 003 bwfinal survival 000 003max daily mortality 10 06

WSSV Litopenaeus vannamei

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Armasus cinereum

Uca panacea

Callinectes sapidus

Litopenaeus setiferus

Uca speciosa

Local decapods exposed to WSSV (China)

0 5 10 15 20 25 30Day

00

01

02

03

04

05

06

07

08

09

10

Surv

ival

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Salt marshes

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Mississippi sound

Jourdan

Biloxi

Pearl

Wolf

Lake Pontchartrain

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Prevalence of WSSV in decapods of Ms Sound

Blue crab (Callinectes sapidus) (83 n=12)

Purple marsh crab (Sesarma reticulatum) (100 n=20)

Gulf mud fiddler crab (Uca longisignalis) (500 n=72)

Panacea sand fiddler crab (U panacea) (108 n=1404)

Mudflat fiddler crab (U rapax) (230 n=88)

Spined fiddler crab (U spinicarpa) (357 n=98)

Red-jointed fiddler crab (U minax) (227 n=22)

Squareback marsh crab (Armasus cinereum) (267 n=30)

Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)

White shrimp (Litopenaeus setiferus) (200 n=40)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Modeling WSSV in communities of decapods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram

λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass

δ η

Susceptible Infected Dead

β

χ

λ

micro

α micro

( ) ( )( )( ) ( )( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( )

1

1

1

1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ λ micro

β χ α micro

α micro η δ

+

+

+

= minus sdot minus minus minus + minus

= + sdot minus minus minus minus minus minus sdot minus sdot

= + minus minus sdot minus sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

Transmission terms - Force of infection λprobability of infection after contact

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 4: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

ldquoBaculoviralesrdquoNimaviruses

HystrosavirusesGpSGHV

MdGHV

WSSV

CunNPV

NeleNPV

AcMNPV

CpGV

HzNV-1

PmNV

GbNV

OrNV

CcBV

TnZBV

CiBV

Bracoviruses

Nudiviruses

Baculoviruses

Wang Y Jehle JA 2009 JIP 101 187-193 Wang Y et al 2011 Vir Gen 42444 ndash 456 Theacutezeacute J et al 2011 PNAS 10815931-35

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Source FAO

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

1950 1970 1990 2010

75

25

Poun

ds (x

109 )

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Shrimp commodity production

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Shrimp Aquaculture SpeciesLitopenaeus vannamei Penaeus monodon

Marsupenaeus japonicusFenneropenaeus chinensis

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

050

100150200250300350400450500

1980 1985 1990 1995

Year

Mill

ions

of P

ound

s

Production of Farmed Shrimp - China

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

19921994 1994 1998

1996

19932002

200219971995

1999

19991999

1999

2005

Spread of WSSV

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Emergence of White spot syndrome virus

1 km

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 Environment changes bringing new contactsMore shrimpPonds built in new areas ndash where shrimp never were or in low numbersMore contact between other (terrestrial) arthropods and shrimp

2 Change in pathogen virulence

3 Introduced from elsewhere

Emergence of White spot syndrome virus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Source FAO

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Hosts of WSSV bull Shrimp

ndash Penaeusbull monodonbull semisulcatus

ndash Farfantepenaeusbull aztecusbull duorarum

ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus

ndash Marsupenaeusbull japonicus

ndash Litopenaeusbull vannameibull stylirostrisbull setiferus

ndash Metapenaeus ensis

ndash Exopalaemonbull orientalis

ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio

bull Crabndash Calappa lophosndash Charybdis

bull feriatabull natotor

ndash Helice spndash Portunus

bull pelagicusbull Sanguineolentus

ndash Callinectes sapidus

ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina

bull Lobsterndash Panuluris

bull longipesbull ornatusbull argus

bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

0

100

200

300

400

500

600

700

800

900

1000

0 3 6 9 12 15 18 21

Num

ber o

f shr

imp

Day

Weight 3 gDensity 550m3

Dose 003 bwfinal survival 000 003max daily mortality 10 06

WSSV Litopenaeus vannamei

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Armasus cinereum

Uca panacea

Callinectes sapidus

Litopenaeus setiferus

Uca speciosa

Local decapods exposed to WSSV (China)

0 5 10 15 20 25 30Day

00

01

02

03

04

05

06

07

08

09

10

Surv

ival

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Salt marshes

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Mississippi sound

Jourdan

Biloxi

Pearl

Wolf

Lake Pontchartrain

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Prevalence of WSSV in decapods of Ms Sound

Blue crab (Callinectes sapidus) (83 n=12)

Purple marsh crab (Sesarma reticulatum) (100 n=20)

Gulf mud fiddler crab (Uca longisignalis) (500 n=72)

Panacea sand fiddler crab (U panacea) (108 n=1404)

Mudflat fiddler crab (U rapax) (230 n=88)

Spined fiddler crab (U spinicarpa) (357 n=98)

Red-jointed fiddler crab (U minax) (227 n=22)

Squareback marsh crab (Armasus cinereum) (267 n=30)

Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)

White shrimp (Litopenaeus setiferus) (200 n=40)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Modeling WSSV in communities of decapods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram

λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass

δ η

Susceptible Infected Dead

β

χ

λ

micro

α micro

( ) ( )( )( ) ( )( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( )

1

1

1

1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ λ micro

β χ α micro

α micro η δ

+

+

+

= minus sdot minus minus minus + minus

= + sdot minus minus minus minus minus minus sdot minus sdot

= + minus minus sdot minus sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

Transmission terms - Force of infection λprobability of infection after contact

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 5: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

Source FAO

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

1950 1970 1990 2010

75

25

Poun

ds (x

109 )

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Shrimp commodity production

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Shrimp Aquaculture SpeciesLitopenaeus vannamei Penaeus monodon

Marsupenaeus japonicusFenneropenaeus chinensis

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

050

100150200250300350400450500

1980 1985 1990 1995

Year

Mill

ions

of P

ound

s

Production of Farmed Shrimp - China

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

19921994 1994 1998

1996

19932002

200219971995

1999

19991999

1999

2005

Spread of WSSV

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Emergence of White spot syndrome virus

1 km

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 Environment changes bringing new contactsMore shrimpPonds built in new areas ndash where shrimp never were or in low numbersMore contact between other (terrestrial) arthropods and shrimp

2 Change in pathogen virulence

3 Introduced from elsewhere

Emergence of White spot syndrome virus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Source FAO

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Hosts of WSSV bull Shrimp

ndash Penaeusbull monodonbull semisulcatus

ndash Farfantepenaeusbull aztecusbull duorarum

ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus

ndash Marsupenaeusbull japonicus

ndash Litopenaeusbull vannameibull stylirostrisbull setiferus

ndash Metapenaeus ensis

ndash Exopalaemonbull orientalis

ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio

bull Crabndash Calappa lophosndash Charybdis

bull feriatabull natotor

ndash Helice spndash Portunus

bull pelagicusbull Sanguineolentus

ndash Callinectes sapidus

ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina

bull Lobsterndash Panuluris

bull longipesbull ornatusbull argus

bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

0

100

200

300

400

500

600

700

800

900

1000

0 3 6 9 12 15 18 21

Num

ber o

f shr

imp

Day

Weight 3 gDensity 550m3

Dose 003 bwfinal survival 000 003max daily mortality 10 06

WSSV Litopenaeus vannamei

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Armasus cinereum

Uca panacea

Callinectes sapidus

Litopenaeus setiferus

Uca speciosa

Local decapods exposed to WSSV (China)

0 5 10 15 20 25 30Day

00

01

02

03

04

05

06

07

08

09

10

Surv

ival

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Salt marshes

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Mississippi sound

Jourdan

Biloxi

Pearl

Wolf

Lake Pontchartrain

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Prevalence of WSSV in decapods of Ms Sound

Blue crab (Callinectes sapidus) (83 n=12)

Purple marsh crab (Sesarma reticulatum) (100 n=20)

Gulf mud fiddler crab (Uca longisignalis) (500 n=72)

Panacea sand fiddler crab (U panacea) (108 n=1404)

Mudflat fiddler crab (U rapax) (230 n=88)

Spined fiddler crab (U spinicarpa) (357 n=98)

Red-jointed fiddler crab (U minax) (227 n=22)

Squareback marsh crab (Armasus cinereum) (267 n=30)

Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)

White shrimp (Litopenaeus setiferus) (200 n=40)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Modeling WSSV in communities of decapods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram

λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass

δ η

Susceptible Infected Dead

β

χ

λ

micro

α micro

( ) ( )( )( ) ( )( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( )

1

1

1

1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ λ micro

β χ α micro

α micro η δ

+

+

+

= minus sdot minus minus minus + minus

= + sdot minus minus minus minus minus minus sdot minus sdot

= + minus minus sdot minus sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

Transmission terms - Force of infection λprobability of infection after contact

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 6: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

Shrimp commodity production

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Shrimp Aquaculture SpeciesLitopenaeus vannamei Penaeus monodon

Marsupenaeus japonicusFenneropenaeus chinensis

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

050

100150200250300350400450500

1980 1985 1990 1995

Year

Mill

ions

of P

ound

s

Production of Farmed Shrimp - China

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

19921994 1994 1998

1996

19932002

200219971995

1999

19991999

1999

2005

Spread of WSSV

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Emergence of White spot syndrome virus

1 km

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 Environment changes bringing new contactsMore shrimpPonds built in new areas ndash where shrimp never were or in low numbersMore contact between other (terrestrial) arthropods and shrimp

2 Change in pathogen virulence

3 Introduced from elsewhere

Emergence of White spot syndrome virus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Source FAO

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Hosts of WSSV bull Shrimp

ndash Penaeusbull monodonbull semisulcatus

ndash Farfantepenaeusbull aztecusbull duorarum

ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus

ndash Marsupenaeusbull japonicus

ndash Litopenaeusbull vannameibull stylirostrisbull setiferus

ndash Metapenaeus ensis

ndash Exopalaemonbull orientalis

ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio

bull Crabndash Calappa lophosndash Charybdis

bull feriatabull natotor

ndash Helice spndash Portunus

bull pelagicusbull Sanguineolentus

ndash Callinectes sapidus

ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina

bull Lobsterndash Panuluris

bull longipesbull ornatusbull argus

bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

0

100

200

300

400

500

600

700

800

900

1000

0 3 6 9 12 15 18 21

Num

ber o

f shr

imp

Day

Weight 3 gDensity 550m3

Dose 003 bwfinal survival 000 003max daily mortality 10 06

WSSV Litopenaeus vannamei

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Armasus cinereum

Uca panacea

Callinectes sapidus

Litopenaeus setiferus

Uca speciosa

Local decapods exposed to WSSV (China)

0 5 10 15 20 25 30Day

00

01

02

03

04

05

06

07

08

09

10

Surv

ival

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Salt marshes

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Mississippi sound

Jourdan

Biloxi

Pearl

Wolf

Lake Pontchartrain

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Prevalence of WSSV in decapods of Ms Sound

Blue crab (Callinectes sapidus) (83 n=12)

Purple marsh crab (Sesarma reticulatum) (100 n=20)

Gulf mud fiddler crab (Uca longisignalis) (500 n=72)

Panacea sand fiddler crab (U panacea) (108 n=1404)

Mudflat fiddler crab (U rapax) (230 n=88)

Spined fiddler crab (U spinicarpa) (357 n=98)

Red-jointed fiddler crab (U minax) (227 n=22)

Squareback marsh crab (Armasus cinereum) (267 n=30)

Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)

White shrimp (Litopenaeus setiferus) (200 n=40)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Modeling WSSV in communities of decapods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram

λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass

δ η

Susceptible Infected Dead

β

χ

λ

micro

α micro

( ) ( )( )( ) ( )( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( )

1

1

1

1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ λ micro

β χ α micro

α micro η δ

+

+

+

= minus sdot minus minus minus + minus

= + sdot minus minus minus minus minus minus sdot minus sdot

= + minus minus sdot minus sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

Transmission terms - Force of infection λprobability of infection after contact

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 7: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

Shrimp Aquaculture SpeciesLitopenaeus vannamei Penaeus monodon

Marsupenaeus japonicusFenneropenaeus chinensis

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

050

100150200250300350400450500

1980 1985 1990 1995

Year

Mill

ions

of P

ound

s

Production of Farmed Shrimp - China

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

19921994 1994 1998

1996

19932002

200219971995

1999

19991999

1999

2005

Spread of WSSV

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Emergence of White spot syndrome virus

1 km

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 Environment changes bringing new contactsMore shrimpPonds built in new areas ndash where shrimp never were or in low numbersMore contact between other (terrestrial) arthropods and shrimp

2 Change in pathogen virulence

3 Introduced from elsewhere

Emergence of White spot syndrome virus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Source FAO

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Hosts of WSSV bull Shrimp

ndash Penaeusbull monodonbull semisulcatus

ndash Farfantepenaeusbull aztecusbull duorarum

ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus

ndash Marsupenaeusbull japonicus

ndash Litopenaeusbull vannameibull stylirostrisbull setiferus

ndash Metapenaeus ensis

ndash Exopalaemonbull orientalis

ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio

bull Crabndash Calappa lophosndash Charybdis

bull feriatabull natotor

ndash Helice spndash Portunus

bull pelagicusbull Sanguineolentus

ndash Callinectes sapidus

ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina

bull Lobsterndash Panuluris

bull longipesbull ornatusbull argus

bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

0

100

200

300

400

500

600

700

800

900

1000

0 3 6 9 12 15 18 21

Num

ber o

f shr

imp

Day

Weight 3 gDensity 550m3

Dose 003 bwfinal survival 000 003max daily mortality 10 06

WSSV Litopenaeus vannamei

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Armasus cinereum

Uca panacea

Callinectes sapidus

Litopenaeus setiferus

Uca speciosa

Local decapods exposed to WSSV (China)

0 5 10 15 20 25 30Day

00

01

02

03

04

05

06

07

08

09

10

Surv

ival

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Salt marshes

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Mississippi sound

Jourdan

Biloxi

Pearl

Wolf

Lake Pontchartrain

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Prevalence of WSSV in decapods of Ms Sound

Blue crab (Callinectes sapidus) (83 n=12)

Purple marsh crab (Sesarma reticulatum) (100 n=20)

Gulf mud fiddler crab (Uca longisignalis) (500 n=72)

Panacea sand fiddler crab (U panacea) (108 n=1404)

Mudflat fiddler crab (U rapax) (230 n=88)

Spined fiddler crab (U spinicarpa) (357 n=98)

Red-jointed fiddler crab (U minax) (227 n=22)

Squareback marsh crab (Armasus cinereum) (267 n=30)

Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)

White shrimp (Litopenaeus setiferus) (200 n=40)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Modeling WSSV in communities of decapods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram

λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass

δ η

Susceptible Infected Dead

β

χ

λ

micro

α micro

( ) ( )( )( ) ( )( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( )

1

1

1

1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ λ micro

β χ α micro

α micro η δ

+

+

+

= minus sdot minus minus minus + minus

= + sdot minus minus minus minus minus minus sdot minus sdot

= + minus minus sdot minus sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

Transmission terms - Force of infection λprobability of infection after contact

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 8: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

050

100150200250300350400450500

1980 1985 1990 1995

Year

Mill

ions

of P

ound

s

Production of Farmed Shrimp - China

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

19921994 1994 1998

1996

19932002

200219971995

1999

19991999

1999

2005

Spread of WSSV

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Emergence of White spot syndrome virus

1 km

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 Environment changes bringing new contactsMore shrimpPonds built in new areas ndash where shrimp never were or in low numbersMore contact between other (terrestrial) arthropods and shrimp

2 Change in pathogen virulence

3 Introduced from elsewhere

Emergence of White spot syndrome virus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Source FAO

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Hosts of WSSV bull Shrimp

ndash Penaeusbull monodonbull semisulcatus

ndash Farfantepenaeusbull aztecusbull duorarum

ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus

ndash Marsupenaeusbull japonicus

ndash Litopenaeusbull vannameibull stylirostrisbull setiferus

ndash Metapenaeus ensis

ndash Exopalaemonbull orientalis

ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio

bull Crabndash Calappa lophosndash Charybdis

bull feriatabull natotor

ndash Helice spndash Portunus

bull pelagicusbull Sanguineolentus

ndash Callinectes sapidus

ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina

bull Lobsterndash Panuluris

bull longipesbull ornatusbull argus

bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

0

100

200

300

400

500

600

700

800

900

1000

0 3 6 9 12 15 18 21

Num

ber o

f shr

imp

Day

Weight 3 gDensity 550m3

Dose 003 bwfinal survival 000 003max daily mortality 10 06

WSSV Litopenaeus vannamei

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Armasus cinereum

Uca panacea

Callinectes sapidus

Litopenaeus setiferus

Uca speciosa

Local decapods exposed to WSSV (China)

0 5 10 15 20 25 30Day

00

01

02

03

04

05

06

07

08

09

10

Surv

ival

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Salt marshes

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Mississippi sound

Jourdan

Biloxi

Pearl

Wolf

Lake Pontchartrain

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Prevalence of WSSV in decapods of Ms Sound

Blue crab (Callinectes sapidus) (83 n=12)

Purple marsh crab (Sesarma reticulatum) (100 n=20)

Gulf mud fiddler crab (Uca longisignalis) (500 n=72)

Panacea sand fiddler crab (U panacea) (108 n=1404)

Mudflat fiddler crab (U rapax) (230 n=88)

Spined fiddler crab (U spinicarpa) (357 n=98)

Red-jointed fiddler crab (U minax) (227 n=22)

Squareback marsh crab (Armasus cinereum) (267 n=30)

Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)

White shrimp (Litopenaeus setiferus) (200 n=40)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Modeling WSSV in communities of decapods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram

λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass

δ η

Susceptible Infected Dead

β

χ

λ

micro

α micro

( ) ( )( )( ) ( )( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( )

1

1

1

1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ λ micro

β χ α micro

α micro η δ

+

+

+

= minus sdot minus minus minus + minus

= + sdot minus minus minus minus minus minus sdot minus sdot

= + minus minus sdot minus sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

Transmission terms - Force of infection λprobability of infection after contact

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 9: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

19921994 1994 1998

1996

19932002

200219971995

1999

19991999

1999

2005

Spread of WSSV

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Emergence of White spot syndrome virus

1 km

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 Environment changes bringing new contactsMore shrimpPonds built in new areas ndash where shrimp never were or in low numbersMore contact between other (terrestrial) arthropods and shrimp

2 Change in pathogen virulence

3 Introduced from elsewhere

Emergence of White spot syndrome virus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Source FAO

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Hosts of WSSV bull Shrimp

ndash Penaeusbull monodonbull semisulcatus

ndash Farfantepenaeusbull aztecusbull duorarum

ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus

ndash Marsupenaeusbull japonicus

ndash Litopenaeusbull vannameibull stylirostrisbull setiferus

ndash Metapenaeus ensis

ndash Exopalaemonbull orientalis

ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio

bull Crabndash Calappa lophosndash Charybdis

bull feriatabull natotor

ndash Helice spndash Portunus

bull pelagicusbull Sanguineolentus

ndash Callinectes sapidus

ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina

bull Lobsterndash Panuluris

bull longipesbull ornatusbull argus

bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

0

100

200

300

400

500

600

700

800

900

1000

0 3 6 9 12 15 18 21

Num

ber o

f shr

imp

Day

Weight 3 gDensity 550m3

Dose 003 bwfinal survival 000 003max daily mortality 10 06

WSSV Litopenaeus vannamei

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Armasus cinereum

Uca panacea

Callinectes sapidus

Litopenaeus setiferus

Uca speciosa

Local decapods exposed to WSSV (China)

0 5 10 15 20 25 30Day

00

01

02

03

04

05

06

07

08

09

10

Surv

ival

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Salt marshes

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Mississippi sound

Jourdan

Biloxi

Pearl

Wolf

Lake Pontchartrain

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Prevalence of WSSV in decapods of Ms Sound

Blue crab (Callinectes sapidus) (83 n=12)

Purple marsh crab (Sesarma reticulatum) (100 n=20)

Gulf mud fiddler crab (Uca longisignalis) (500 n=72)

Panacea sand fiddler crab (U panacea) (108 n=1404)

Mudflat fiddler crab (U rapax) (230 n=88)

Spined fiddler crab (U spinicarpa) (357 n=98)

Red-jointed fiddler crab (U minax) (227 n=22)

Squareback marsh crab (Armasus cinereum) (267 n=30)

Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)

White shrimp (Litopenaeus setiferus) (200 n=40)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Modeling WSSV in communities of decapods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram

λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass

δ η

Susceptible Infected Dead

β

χ

λ

micro

α micro

( ) ( )( )( ) ( )( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( )

1

1

1

1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ λ micro

β χ α micro

α micro η δ

+

+

+

= minus sdot minus minus minus + minus

= + sdot minus minus minus minus minus minus sdot minus sdot

= + minus minus sdot minus sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

Transmission terms - Force of infection λprobability of infection after contact

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 10: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

Emergence of White spot syndrome virus

1 km

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 Environment changes bringing new contactsMore shrimpPonds built in new areas ndash where shrimp never were or in low numbersMore contact between other (terrestrial) arthropods and shrimp

2 Change in pathogen virulence

3 Introduced from elsewhere

Emergence of White spot syndrome virus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Source FAO

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Hosts of WSSV bull Shrimp

ndash Penaeusbull monodonbull semisulcatus

ndash Farfantepenaeusbull aztecusbull duorarum

ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus

ndash Marsupenaeusbull japonicus

ndash Litopenaeusbull vannameibull stylirostrisbull setiferus

ndash Metapenaeus ensis

ndash Exopalaemonbull orientalis

ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio

bull Crabndash Calappa lophosndash Charybdis

bull feriatabull natotor

ndash Helice spndash Portunus

bull pelagicusbull Sanguineolentus

ndash Callinectes sapidus

ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina

bull Lobsterndash Panuluris

bull longipesbull ornatusbull argus

bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

0

100

200

300

400

500

600

700

800

900

1000

0 3 6 9 12 15 18 21

Num

ber o

f shr

imp

Day

Weight 3 gDensity 550m3

Dose 003 bwfinal survival 000 003max daily mortality 10 06

WSSV Litopenaeus vannamei

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Armasus cinereum

Uca panacea

Callinectes sapidus

Litopenaeus setiferus

Uca speciosa

Local decapods exposed to WSSV (China)

0 5 10 15 20 25 30Day

00

01

02

03

04

05

06

07

08

09

10

Surv

ival

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Salt marshes

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Mississippi sound

Jourdan

Biloxi

Pearl

Wolf

Lake Pontchartrain

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Prevalence of WSSV in decapods of Ms Sound

Blue crab (Callinectes sapidus) (83 n=12)

Purple marsh crab (Sesarma reticulatum) (100 n=20)

Gulf mud fiddler crab (Uca longisignalis) (500 n=72)

Panacea sand fiddler crab (U panacea) (108 n=1404)

Mudflat fiddler crab (U rapax) (230 n=88)

Spined fiddler crab (U spinicarpa) (357 n=98)

Red-jointed fiddler crab (U minax) (227 n=22)

Squareback marsh crab (Armasus cinereum) (267 n=30)

Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)

White shrimp (Litopenaeus setiferus) (200 n=40)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Modeling WSSV in communities of decapods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram

λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass

δ η

Susceptible Infected Dead

β

χ

λ

micro

α micro

( ) ( )( )( ) ( )( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( )

1

1

1

1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ λ micro

β χ α micro

α micro η δ

+

+

+

= minus sdot minus minus minus + minus

= + sdot minus minus minus minus minus minus sdot minus sdot

= + minus minus sdot minus sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

Transmission terms - Force of infection λprobability of infection after contact

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 11: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

1 Environment changes bringing new contactsMore shrimpPonds built in new areas ndash where shrimp never were or in low numbersMore contact between other (terrestrial) arthropods and shrimp

2 Change in pathogen virulence

3 Introduced from elsewhere

Emergence of White spot syndrome virus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Source FAO

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Hosts of WSSV bull Shrimp

ndash Penaeusbull monodonbull semisulcatus

ndash Farfantepenaeusbull aztecusbull duorarum

ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus

ndash Marsupenaeusbull japonicus

ndash Litopenaeusbull vannameibull stylirostrisbull setiferus

ndash Metapenaeus ensis

ndash Exopalaemonbull orientalis

ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio

bull Crabndash Calappa lophosndash Charybdis

bull feriatabull natotor

ndash Helice spndash Portunus

bull pelagicusbull Sanguineolentus

ndash Callinectes sapidus

ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina

bull Lobsterndash Panuluris

bull longipesbull ornatusbull argus

bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

0

100

200

300

400

500

600

700

800

900

1000

0 3 6 9 12 15 18 21

Num

ber o

f shr

imp

Day

Weight 3 gDensity 550m3

Dose 003 bwfinal survival 000 003max daily mortality 10 06

WSSV Litopenaeus vannamei

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Armasus cinereum

Uca panacea

Callinectes sapidus

Litopenaeus setiferus

Uca speciosa

Local decapods exposed to WSSV (China)

0 5 10 15 20 25 30Day

00

01

02

03

04

05

06

07

08

09

10

Surv

ival

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Salt marshes

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Mississippi sound

Jourdan

Biloxi

Pearl

Wolf

Lake Pontchartrain

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Prevalence of WSSV in decapods of Ms Sound

Blue crab (Callinectes sapidus) (83 n=12)

Purple marsh crab (Sesarma reticulatum) (100 n=20)

Gulf mud fiddler crab (Uca longisignalis) (500 n=72)

Panacea sand fiddler crab (U panacea) (108 n=1404)

Mudflat fiddler crab (U rapax) (230 n=88)

Spined fiddler crab (U spinicarpa) (357 n=98)

Red-jointed fiddler crab (U minax) (227 n=22)

Squareback marsh crab (Armasus cinereum) (267 n=30)

Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)

White shrimp (Litopenaeus setiferus) (200 n=40)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Modeling WSSV in communities of decapods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram

λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass

δ η

Susceptible Infected Dead

β

χ

λ

micro

α micro

( ) ( )( )( ) ( )( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( )

1

1

1

1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ λ micro

β χ α micro

α micro η δ

+

+

+

= minus sdot minus minus minus + minus

= + sdot minus minus minus minus minus minus sdot minus sdot

= + minus minus sdot minus sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

Transmission terms - Force of infection λprobability of infection after contact

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 12: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

Source FAO

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

Worlds Production of Penaeid Shrimp

AquacultureCaptureTotal

0

5

10

15

Poun

ds (x

109 )

1950 1970 1990 2010

75

25

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Hosts of WSSV bull Shrimp

ndash Penaeusbull monodonbull semisulcatus

ndash Farfantepenaeusbull aztecusbull duorarum

ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus

ndash Marsupenaeusbull japonicus

ndash Litopenaeusbull vannameibull stylirostrisbull setiferus

ndash Metapenaeus ensis

ndash Exopalaemonbull orientalis

ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio

bull Crabndash Calappa lophosndash Charybdis

bull feriatabull natotor

ndash Helice spndash Portunus

bull pelagicusbull Sanguineolentus

ndash Callinectes sapidus

ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina

bull Lobsterndash Panuluris

bull longipesbull ornatusbull argus

bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

0

100

200

300

400

500

600

700

800

900

1000

0 3 6 9 12 15 18 21

Num

ber o

f shr

imp

Day

Weight 3 gDensity 550m3

Dose 003 bwfinal survival 000 003max daily mortality 10 06

WSSV Litopenaeus vannamei

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Armasus cinereum

Uca panacea

Callinectes sapidus

Litopenaeus setiferus

Uca speciosa

Local decapods exposed to WSSV (China)

0 5 10 15 20 25 30Day

00

01

02

03

04

05

06

07

08

09

10

Surv

ival

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Salt marshes

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Mississippi sound

Jourdan

Biloxi

Pearl

Wolf

Lake Pontchartrain

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Prevalence of WSSV in decapods of Ms Sound

Blue crab (Callinectes sapidus) (83 n=12)

Purple marsh crab (Sesarma reticulatum) (100 n=20)

Gulf mud fiddler crab (Uca longisignalis) (500 n=72)

Panacea sand fiddler crab (U panacea) (108 n=1404)

Mudflat fiddler crab (U rapax) (230 n=88)

Spined fiddler crab (U spinicarpa) (357 n=98)

Red-jointed fiddler crab (U minax) (227 n=22)

Squareback marsh crab (Armasus cinereum) (267 n=30)

Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)

White shrimp (Litopenaeus setiferus) (200 n=40)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Modeling WSSV in communities of decapods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram

λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass

δ η

Susceptible Infected Dead

β

χ

λ

micro

α micro

( ) ( )( )( ) ( )( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( )

1

1

1

1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ λ micro

β χ α micro

α micro η δ

+

+

+

= minus sdot minus minus minus + minus

= + sdot minus minus minus minus minus minus sdot minus sdot

= + minus minus sdot minus sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

Transmission terms - Force of infection λprobability of infection after contact

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 13: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Hosts of WSSV bull Shrimp

ndash Penaeusbull monodonbull semisulcatus

ndash Farfantepenaeusbull aztecusbull duorarum

ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus

ndash Marsupenaeusbull japonicus

ndash Litopenaeusbull vannameibull stylirostrisbull setiferus

ndash Metapenaeus ensis

ndash Exopalaemonbull orientalis

ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio

bull Crabndash Calappa lophosndash Charybdis

bull feriatabull natotor

ndash Helice spndash Portunus

bull pelagicusbull Sanguineolentus

ndash Callinectes sapidus

ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina

bull Lobsterndash Panuluris

bull longipesbull ornatusbull argus

bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

0

100

200

300

400

500

600

700

800

900

1000

0 3 6 9 12 15 18 21

Num

ber o

f shr

imp

Day

Weight 3 gDensity 550m3

Dose 003 bwfinal survival 000 003max daily mortality 10 06

WSSV Litopenaeus vannamei

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Armasus cinereum

Uca panacea

Callinectes sapidus

Litopenaeus setiferus

Uca speciosa

Local decapods exposed to WSSV (China)

0 5 10 15 20 25 30Day

00

01

02

03

04

05

06

07

08

09

10

Surv

ival

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Salt marshes

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Mississippi sound

Jourdan

Biloxi

Pearl

Wolf

Lake Pontchartrain

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Prevalence of WSSV in decapods of Ms Sound

Blue crab (Callinectes sapidus) (83 n=12)

Purple marsh crab (Sesarma reticulatum) (100 n=20)

Gulf mud fiddler crab (Uca longisignalis) (500 n=72)

Panacea sand fiddler crab (U panacea) (108 n=1404)

Mudflat fiddler crab (U rapax) (230 n=88)

Spined fiddler crab (U spinicarpa) (357 n=98)

Red-jointed fiddler crab (U minax) (227 n=22)

Squareback marsh crab (Armasus cinereum) (267 n=30)

Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)

White shrimp (Litopenaeus setiferus) (200 n=40)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Modeling WSSV in communities of decapods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram

λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass

δ η

Susceptible Infected Dead

β

χ

λ

micro

α micro

( ) ( )( )( ) ( )( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( )

1

1

1

1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ λ micro

β χ α micro

α micro η δ

+

+

+

= minus sdot minus minus minus + minus

= + sdot minus minus minus minus minus minus sdot minus sdot

= + minus minus sdot minus sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

Transmission terms - Force of infection λprobability of infection after contact

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 14: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

Hosts of WSSV bull Shrimp

ndash Penaeusbull monodonbull semisulcatus

ndash Farfantepenaeusbull aztecusbull duorarum

ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus

ndash Marsupenaeusbull japonicus

ndash Litopenaeusbull vannameibull stylirostrisbull setiferus

ndash Metapenaeus ensis

ndash Exopalaemonbull orientalis

ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio

bull Crabndash Calappa lophosndash Charybdis

bull feriatabull natotor

ndash Helice spndash Portunus

bull pelagicusbull Sanguineolentus

ndash Callinectes sapidus

ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina

bull Lobsterndash Panuluris

bull longipesbull ornatusbull argus

bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

0

100

200

300

400

500

600

700

800

900

1000

0 3 6 9 12 15 18 21

Num

ber o

f shr

imp

Day

Weight 3 gDensity 550m3

Dose 003 bwfinal survival 000 003max daily mortality 10 06

WSSV Litopenaeus vannamei

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Armasus cinereum

Uca panacea

Callinectes sapidus

Litopenaeus setiferus

Uca speciosa

Local decapods exposed to WSSV (China)

0 5 10 15 20 25 30Day

00

01

02

03

04

05

06

07

08

09

10

Surv

ival

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Salt marshes

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Mississippi sound

Jourdan

Biloxi

Pearl

Wolf

Lake Pontchartrain

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Prevalence of WSSV in decapods of Ms Sound

Blue crab (Callinectes sapidus) (83 n=12)

Purple marsh crab (Sesarma reticulatum) (100 n=20)

Gulf mud fiddler crab (Uca longisignalis) (500 n=72)

Panacea sand fiddler crab (U panacea) (108 n=1404)

Mudflat fiddler crab (U rapax) (230 n=88)

Spined fiddler crab (U spinicarpa) (357 n=98)

Red-jointed fiddler crab (U minax) (227 n=22)

Squareback marsh crab (Armasus cinereum) (267 n=30)

Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)

White shrimp (Litopenaeus setiferus) (200 n=40)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Modeling WSSV in communities of decapods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram

λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass

δ η

Susceptible Infected Dead

β

χ

λ

micro

α micro

( ) ( )( )( ) ( )( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( )

1

1

1

1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ λ micro

β χ α micro

α micro η δ

+

+

+

= minus sdot minus minus minus + minus

= + sdot minus minus minus minus minus minus sdot minus sdot

= + minus minus sdot minus sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

Transmission terms - Force of infection λprobability of infection after contact

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 15: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

0

100

200

300

400

500

600

700

800

900

1000

0 3 6 9 12 15 18 21

Num

ber o

f shr

imp

Day

Weight 3 gDensity 550m3

Dose 003 bwfinal survival 000 003max daily mortality 10 06

WSSV Litopenaeus vannamei

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Armasus cinereum

Uca panacea

Callinectes sapidus

Litopenaeus setiferus

Uca speciosa

Local decapods exposed to WSSV (China)

0 5 10 15 20 25 30Day

00

01

02

03

04

05

06

07

08

09

10

Surv

ival

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Salt marshes

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Mississippi sound

Jourdan

Biloxi

Pearl

Wolf

Lake Pontchartrain

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Prevalence of WSSV in decapods of Ms Sound

Blue crab (Callinectes sapidus) (83 n=12)

Purple marsh crab (Sesarma reticulatum) (100 n=20)

Gulf mud fiddler crab (Uca longisignalis) (500 n=72)

Panacea sand fiddler crab (U panacea) (108 n=1404)

Mudflat fiddler crab (U rapax) (230 n=88)

Spined fiddler crab (U spinicarpa) (357 n=98)

Red-jointed fiddler crab (U minax) (227 n=22)

Squareback marsh crab (Armasus cinereum) (267 n=30)

Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)

White shrimp (Litopenaeus setiferus) (200 n=40)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Modeling WSSV in communities of decapods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram

λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass

δ η

Susceptible Infected Dead

β

χ

λ

micro

α micro

( ) ( )( )( ) ( )( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( )

1

1

1

1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ λ micro

β χ α micro

α micro η δ

+

+

+

= minus sdot minus minus minus + minus

= + sdot minus minus minus minus minus minus sdot minus sdot

= + minus minus sdot minus sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

Transmission terms - Force of infection λprobability of infection after contact

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 16: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

Armasus cinereum

Uca panacea

Callinectes sapidus

Litopenaeus setiferus

Uca speciosa

Local decapods exposed to WSSV (China)

0 5 10 15 20 25 30Day

00

01

02

03

04

05

06

07

08

09

10

Surv

ival

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Salt marshes

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Mississippi sound

Jourdan

Biloxi

Pearl

Wolf

Lake Pontchartrain

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Prevalence of WSSV in decapods of Ms Sound

Blue crab (Callinectes sapidus) (83 n=12)

Purple marsh crab (Sesarma reticulatum) (100 n=20)

Gulf mud fiddler crab (Uca longisignalis) (500 n=72)

Panacea sand fiddler crab (U panacea) (108 n=1404)

Mudflat fiddler crab (U rapax) (230 n=88)

Spined fiddler crab (U spinicarpa) (357 n=98)

Red-jointed fiddler crab (U minax) (227 n=22)

Squareback marsh crab (Armasus cinereum) (267 n=30)

Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)

White shrimp (Litopenaeus setiferus) (200 n=40)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Modeling WSSV in communities of decapods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram

λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass

δ η

Susceptible Infected Dead

β

χ

λ

micro

α micro

( ) ( )( )( ) ( )( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( )

1

1

1

1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ λ micro

β χ α micro

α micro η δ

+

+

+

= minus sdot minus minus minus + minus

= + sdot minus minus minus minus minus minus sdot minus sdot

= + minus minus sdot minus sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

Transmission terms - Force of infection λprobability of infection after contact

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 17: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

Salt marshes

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Mississippi sound

Jourdan

Biloxi

Pearl

Wolf

Lake Pontchartrain

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Prevalence of WSSV in decapods of Ms Sound

Blue crab (Callinectes sapidus) (83 n=12)

Purple marsh crab (Sesarma reticulatum) (100 n=20)

Gulf mud fiddler crab (Uca longisignalis) (500 n=72)

Panacea sand fiddler crab (U panacea) (108 n=1404)

Mudflat fiddler crab (U rapax) (230 n=88)

Spined fiddler crab (U spinicarpa) (357 n=98)

Red-jointed fiddler crab (U minax) (227 n=22)

Squareback marsh crab (Armasus cinereum) (267 n=30)

Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)

White shrimp (Litopenaeus setiferus) (200 n=40)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Modeling WSSV in communities of decapods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram

λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass

δ η

Susceptible Infected Dead

β

χ

λ

micro

α micro

( ) ( )( )( ) ( )( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( )

1

1

1

1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ λ micro

β χ α micro

α micro η δ

+

+

+

= minus sdot minus minus minus + minus

= + sdot minus minus minus minus minus minus sdot minus sdot

= + minus minus sdot minus sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

Transmission terms - Force of infection λprobability of infection after contact

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 18: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

Mississippi sound

Jourdan

Biloxi

Pearl

Wolf

Lake Pontchartrain

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Prevalence of WSSV in decapods of Ms Sound

Blue crab (Callinectes sapidus) (83 n=12)

Purple marsh crab (Sesarma reticulatum) (100 n=20)

Gulf mud fiddler crab (Uca longisignalis) (500 n=72)

Panacea sand fiddler crab (U panacea) (108 n=1404)

Mudflat fiddler crab (U rapax) (230 n=88)

Spined fiddler crab (U spinicarpa) (357 n=98)

Red-jointed fiddler crab (U minax) (227 n=22)

Squareback marsh crab (Armasus cinereum) (267 n=30)

Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)

White shrimp (Litopenaeus setiferus) (200 n=40)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Modeling WSSV in communities of decapods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram

λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass

δ η

Susceptible Infected Dead

β

χ

λ

micro

α micro

( ) ( )( )( ) ( )( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( )

1

1

1

1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ λ micro

β χ α micro

α micro η δ

+

+

+

= minus sdot minus minus minus + minus

= + sdot minus minus minus minus minus minus sdot minus sdot

= + minus minus sdot minus sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

Transmission terms - Force of infection λprobability of infection after contact

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 19: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

Prevalence of WSSV in decapods of Ms Sound

Blue crab (Callinectes sapidus) (83 n=12)

Purple marsh crab (Sesarma reticulatum) (100 n=20)

Gulf mud fiddler crab (Uca longisignalis) (500 n=72)

Panacea sand fiddler crab (U panacea) (108 n=1404)

Mudflat fiddler crab (U rapax) (230 n=88)

Spined fiddler crab (U spinicarpa) (357 n=98)

Red-jointed fiddler crab (U minax) (227 n=22)

Squareback marsh crab (Armasus cinereum) (267 n=30)

Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)

White shrimp (Litopenaeus setiferus) (200 n=40)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Modeling WSSV in communities of decapods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram

λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass

δ η

Susceptible Infected Dead

β

χ

λ

micro

α micro

( ) ( )( )( ) ( )( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( )

1

1

1

1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ λ micro

β χ α micro

α micro η δ

+

+

+

= minus sdot minus minus minus + minus

= + sdot minus minus minus minus minus minus sdot minus sdot

= + minus minus sdot minus sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

Transmission terms - Force of infection λprobability of infection after contact

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 20: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

Modeling WSSV in communities of decapods

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram

λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass

δ η

Susceptible Infected Dead

β

χ

λ

micro

α micro

( ) ( )( )( ) ( )( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( )

1

1

1

1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ λ micro

β χ α micro

α micro η δ

+

+

+

= minus sdot minus minus minus + minus

= + sdot minus minus minus minus minus minus sdot minus sdot

= + minus minus sdot minus sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

Transmission terms - Force of infection λprobability of infection after contact

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 21: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

WSSV life cycle diagram

λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass

δ η

Susceptible Infected Dead

β

χ

λ

micro

α micro

( ) ( )( )( ) ( )( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( )

1

1

1

1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ λ micro

β χ α micro

α micro η δ

+

+

+

= minus sdot minus minus minus + minus

= + sdot minus minus minus minus minus minus sdot minus sdot

= + minus minus sdot minus sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

Transmission terms - Force of infection λprobability of infection after contact

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 22: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

Transmission terms - Force of infection λprobability of infection after contact

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 23: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

( )1 1 Iλ β= minus minus

( )Iλ β= sdot

Force of InfectionProbability of infection after contact with all infecteds

Ross

Reed-Frost

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 24: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

1 2 3 4 5 6 7

1 11 12 13 14 15 16 17

2 21 22 23 24 25 26 27

3 31 32 33 34 35 36 37

S S S S S S S

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

I SI SI SI SI SI SI SI

( )1-

t t t tS S S Iβ

+= sdot sdot

RossKermack-McKendrick

If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I

May have more infects than susceptiblesSome transmissions are to the same susceptible

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 25: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

2(1 )βminus

1 βminusβ 1 βminusβ

21 (1 )βminus minus

3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ

Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)

βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ

1- (1 )(1 ) t

t t tIS S S β+

= sdot minus minusReed-Frost

Black-Singer

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 26: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

Epidemic models ndash parameter estimates

( ) ( )( )( ) ( )( )

( ) ( )( )

1

1

1

1 1 1

1 1 1

1 1 1

t t

t t

I Dt t t

I Dt t t t

t t t t

S S S

I I S I

D D I D

β χ

β χ α

α η δ

+

+

+

= minus sdot minus minus minus

= + sdot minus minus minus minus sdot

= + sdot minus minus minus sdot minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 27: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

If t = 1 and I0 = 1

1

0

1 ss

β

= minus

The proportion infected after exposure to one infected shrimpβ

Parameter estimates ndash transmission (β χ)

1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus

Solve for β

1

1

0

0

ln(1) 1 exp

tSS

= minus

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 28: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 29: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 30: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

Parameter estimates ndash transmission (β χ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 31: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors

Parameter estimates ndash transmission (β χ) and virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 32: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

1t t tI I I α+ = minus sdot

0

10

20

30

40

0 4 8 12 16Time (h)

Surv

ival

Parameter estimates ndash virulence (α)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 33: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

decomposition

transmission decreases by 48 per day

y-intercept = 0499

0 4 8 12Days after death

00

02

04

06

08

10

Tran

smis

sion

χ

Parameter estimates ndash decay of transmission (δ)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 34: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

Parameter estimates η consumption of shrimp

24 shrimp12 shrimp

6 shrimp1 shrimp

FedFasted

decrease per hr (day) decrease per hr (day)

0 10 20 30Time (hr)

00

02

04

06

08

10

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

10

0 10 20 30Time (hr)

00

02

04

06

08

Prop

ortio

n B

iom

ass

0 10 20 300 10 20 300 10 20 300 10 20 30

17 (99)30 (100)34 (100)33 (100)

6 (79)11 (94)11 (94)12 (96)

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 35: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

Parameter estimates consumption (η) amp decomposition (δ) combined

048 + 100 - 10 048= 100

048 + 79 - 7948= 089

An infected dead shrimp retains about 0 ndash 10 of its infectivity per day

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 36: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

State Duration Transmission Product

Live Infected β

Dead Infected χ( )( )

11 1 1δ ηminus minus minus

βα

( )( )1 1 1χδ ηminus minus minus

0R β χα δ η δ η

= ++ minus sdot

Life table of infection

001 06 0904 05 09 05 09

R = + =+ minus sdot

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 37: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

WSSV life cycle diagram3-host community

Susceptible

Susceptible

Susceptible Infected

Infected

Infected Dead

Dead

Dead

β31

χ31

χ11

β11λ1

λ2

λ3

micro1

micro2

micro3

β12 β21 χ21

α1 micro1

α2 micro2

α3 micro3

χ12

δ1 η1

δ2 η2

δ3 η3χ33

β33

χ13

β13

χ22

β32χ32

β22

χ23β23

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38
Page 38: WSSV - White spot syndrome virus · 2015-05-13 · WSSV - White spot syndrome virus. RCN Marine Disease Modeling and Transmission Workshop – May 2015

( ) ( )

( ) ( )( ) ( )

( ) ( )

( ) ( )( ) ( )

3

1 11

3

1 1 11

1

3

2 21

3

2 2 21

2

3

1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1

i i

i i

i i

i i

I Di i

i

I Di i

i

I Di i

i

I Di i

i

β χ

β χ α

α δ η

β χ

β χ α

α δ η

β

=

=

=

=

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus sdot minus

minus minus sdot minus minus

minus minus sdot minus

minus

prod

prod

prod

prod

( ) ( )

( ) ( )( ) ( )

1

1

1

2

2

2

3

33

331

3

3 3 31

3

1 0 0

0 0 0 0 0 0 1 1 1 1 0

0 0 0 0 0 0 0 1 1 1

i i

i i

I Di i

i

I Di i

i

SIDSIDSIDχ

β χ α

α δ η

=

=

sdot

sdot minus

minus minus sdot minus minus minus minus sdot minus

prod

prod

WSSV 3-host community matrix model

RCN Marine Disease Modeling and Transmission Workshop ndash May 2015

  • Slide Number 1
  • Slide Number 2
  • Slide Number 3
  • Slide Number 4
  • Slide Number 5
  • Slide Number 6
  • Slide Number 7
  • Slide Number 8
  • Slide Number 9
  • Emergence of White spot syndrome virus
  • Slide Number 11
  • Slide Number 12
  • Slide Number 13
  • Hosts of WSSV
  • WSSV Litopenaeus vannamei
  • Slide Number 16
  • Slide Number 17
  • Slide Number 18
  • Slide Number 19
  • Slide Number 20
  • Slide Number 21
  • Slide Number 22
  • Slide Number 23
  • Slide Number 24
  • Slide Number 25
  • Slide Number 26
  • Slide Number 27
  • Slide Number 28
  • Slide Number 29
  • Slide Number 30
  • Slide Number 31
  • Slide Number 32
  • Slide Number 33
  • Slide Number 34
  • Slide Number 35
  • Slide Number 36
  • Slide Number 37
  • Slide Number 38