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“To cull or not to cull, this is the problem”:
undersired effects of animals removal to eraticate diseases in widlife populations
(the adaptive dynamics of CSF in wild boars)
EEE - ICTP
Trieste April 13-15 2005
Giulio De LeoDipartimento di Scienze Ambientali
Università degli Studi di Parma - Italy
Thanks to A.Dobson and M. Pascualand to the NCEAS WG on Seasonality and Infectious diseases
cIIISI
cSISSGSo
o
)( c :hunting rate [t-1]
If the case of no culling (c=0):
Let’s take the Classical Swine Fever (CSF) as a reference disease
K
R0
10 R
TKK
It can be proven that it is possible to eradicate the disease if: c > r [1- 1/Ro]
Basics of Classical swine fever (CSF) or Hog Cholera
• A highly contagious disease due to a RNA virus, Family TOGAVIRIDAE, Genus Pestivirus;
• It is a List A disease in the OIE Classification of Diseases
• Suidae are the sole natural hosts;
Basics of Classical swine fever (CSF) or Hog Cholera
• Infected animals may shed large amounts of virus for 20 - 40 days through oronasal and lacrimal secretions, urine and feces
• The direct contact between infected and susceptible animals is the principle means of viral transmission;
Basics of Classical swine fever (CSF) or Hog CholeraEpidemiology
• CSF causes high morbidity and mortality (up to 90%) during the first epidemic wave…
but low virulent strains can be isolated in wild boars in the following endemic phase;– Acute infections – Chronic infections /endemic phases
CSF distribution(OEI 1995-1997)
CSF outbreaks in wild boars1990-2001
Why people care about CSF in EU?
• Wild boars are blamed to be the reservoir of CSF
UE Damages from CSF between 1993 and 2000
Country N. Swines removed ( = 1 milion specimen)
NL 10
Germany 2
Spaain 1
Belgium < 1
Italy < 1
A 100 kg pig ~ €150,00
• which is easier to say than to do it…
• The EU supports a program to eradicate the virus from wild boar mainly based on reducing population density through culling
– What to cull?
– Where to cull?
– When to cull?
– How to cull?
0 0.1 0.2 0.3 0.4 0.50
0.05
0.1
0.15
Culling rate [y-1]
tras
mis
sion
rat
es
c( )
a c( )
c
.
Culling rate [y-1]
Drawbacks of culling (1/2)as reported by the Italian Wildlife National Service (INFS)
• It may push hosts out of their natural home range, thus fostering disease spread
~ 20% increase of culling rate
~ 60% reduction of population density
with respect to constant
Ro
Culling rate [y-1]
0 0.1 0.2 0.3 0.4 0.50
2
4
6reproduct ive number
Cuilling Rate
1
Ro c( )
Rao c( )
ca ce
c
ce caca
18 .9%
.
Seq ce( )
K8.8%
Seq 0( )
K21 .7%
Saeq ca( )
K23 .3%
1
Drawbacks of culling (2/2)• It may push hosts out of their natural
home range, thus fostering disease spread• If culling is focused mainly on old (low susceptible)
hosts, it may change population age structure in favor of more susceptible yearlings
• Given the existence of multiple strains of CSF (Biagetti et al. 2001), a change in host density may foster the selection of less virulent but more persistent strains, thus making culling more costly and ineffective
• Research questions:– Is it possible? – If positive, under which conditions?– Which are the consequences?
A simple two-strains competition model
• Hosts I1 infected
with a Low Virulent Strain (LVS)
small 1
• Hosts I2 infected
with a High Virulent Strain (HVS) large 2
S
I2
I1
low virulent strain
(small 1)
highly virulent strain
(large 2)
c
cc
12 is the super-infection
coefficient
The new equations (LVS vs. HVS ):
S' =G(S) - 1I1S - 2I2S - cS
I1' = 1I1S - (1 + + c) I1 12I1I2
I2' = 2I2S - (2 + + c) I2 + 12I1I2
Assumptions on the LVS vs. HVS
• Disease induced mortality (virulence)
• 1 << 2
• Transmission rate
• 1 2 12 0
Basic epidemiological implications of the above assumptions
• Basic Reproductive rate (LVS vs. HVS)
R01 =
1K
1 + >
2K
2 + = R02
• Threshold density for disease eradication
KT1< KT2
LVS can persist in a very sparse population
Su
scep
tib
les (
S)
(over 2
20
km2 )
0
100
200
300
400
time [month]
0 20 40 60 80 100
In
fecte
d (
I)
0
25
50
75
100
S
I1I2
time [month]
0 5 10 15 20
0 5 10 15 20
In
fecte
d (
I)
0.1
1
10
100
I1
I2
(LVS)
(LVS)
(HVS)
(HVS)
Further epidemiological implications
• If there is no super-infection (12=0)
LVS always outcompetes HVS
If there is super-infection (12 >0)
12 <
1 KT
I*1
• If LVS outcompetes HVS
12 >
2 KT
I*2
• If HVS outcompetes LVS
1 KT
I*1
<12<
2 KT
I*2
• If LVS and HVS coexist
KT = KT2 – KT1 – c (1/1 – 1/2)
I*1 =
G(KT1+ c/1)
1 (K T1+ c/1) - c/1 I*
2 = G(KT2 + c/2)
2 (KT2+ c/2) - c/2
where
Further epidemiological implications
• If hog population density K (as well 12)
is sufficiently high, then
HVS can coexist with, or even outcompete LVS
decreasing population density by culling migh
increase the chance of LVS to outcompete HVS
Epidemiology of classical swine fever in wild boars of Eastern Sardinia LVS
HVS
from a field survey by Guberti (1998)and Artois et al. (2002)
Parameters Symbol Value Unit
Hog carrying capacity K 600 hosts over 220 km2
Pop. growth rate r 0.5 Years-1
Natural Mortality 0.2 Years-1
Disease induced mortality
1 5 Years-1
Transmission rate 1 0.04 [# infected 1] -1 y-1
Reproductive rate Ro1 4.6
Disease induced mortality
2 15 Years-1
Transmission rate 2 0.06 [#infected 2] -1 y-1
Reproductive rate Ro2 2.37
Superinfection coeffi cient
12 0.84 [#infected 1] -1 y-1
Removal rate
Prevalence at the equilibrium as a function of culling rate, when the two strains are isolated
Prevalence at equilibrium as a function of harvesting effort for two competing strains
Number of infected individuals
The SI2R model(Susceptible-Infected-Recovered)
S
I2
I1
LVS(small1)
HVS(large 2)R
c
cc
c
Conclusions• It is possible that the reduction of host density by culling
may indeed foster the selection of less virulent strains • This in turn would reduce the threshold host density for
disease eradication• If this happens, the harvesting effort required to completely
eradicate the disease will be higher than initially expected• If culling effort is not large enough, the net effect of this
policy is to increase both prevalence and the number of infected hosts
• The harvesting effort required for the eradication of the least virulent strains may be unrealistically high (or too costly)
Further developments
• Analyse pop.dynamics by using a stochastic (possibly spatially explicit, seasonal) version of the model
• Introduce age structure and age-depedent epidemiological parameters
Su
scep
tib
les (
S)
(over 2
20
km2 )
0
100
200
300
400
time [month]
0 20 40 60 80 100
In
fecte
d (
I)
0
25
50
75
100
S
I1I2
time [month]
0 5 10 15 20
0 5 10 15 20
In
fecte
d (
I)
0.1
1
10
100
I1
I2
(LVS)
(LVS)
(HVS)
(HVS)
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