Mathematical modeling of ranavirus ecology

Mathematical Modeling ofMathematical Modeling of Ranavirus Ecology

Dr. Amanda L. J. DuffusAssistant Professor of Biology

Department of Biology

Gordon State College, Barnesville, GA

[email protected]

Outline

• Potential Role of Disease in Population Declines

• Ranaviral Disease in UK Common Frogs

• Model Development

• Model Utility

• Conclusions

Potential Role of Disease in DeclinesPotential Role of Disease in Declines

• Disease is naturally occurringDisease is naturally occurring• Can provide a way to maintain diversity• Disease can cause declines &/or extinction• Disease can cause declines &/or extinction

Al lt iAlso can result in:• Higher mortality rates• Decreased reproduction• Decrease other aspects of fitness

Ranaviral Disease in UK Common FrogsRanaviral Disease in UK Common Frogs

• Two different forms of disease:Two different forms of disease:– Ulcerative

Hemorrhagic– Hemorrhagic

– Not mutually exclusive


A A CunninghamA.A. Cunningham



• Adults are the most commonly affected lifeAdults are the most commonly affected life history stage (Duffus et al. 2013)– Limited evidence of infection in tadpoles– Limited evidence of infection in tadpoles

– No evidence of infections in eggs


• Long term data setLong term data set– Know that ranaviral infections can persist in populations for long periods of timepopulations for long periods of time

• Ranavirus emergence has been associated• Ranavirus emergence has been associated with population declines in common frogs (Teacher et al. 2010)( )


• Interesting Questions:Interesting Questions:– Can the ranavirus persist in these populations of common frogs if only adult to adult transmissioncommon frogs if only adult to adult transmission occurs?

– Can both disease syndromes be maintained in aCan both disease syndromes be maintained in a population?

Interesting Question 1Interesting Question 1

Can the ranavirus persist in these populations of common frogs if only adult to adult transmissioncommon frogs if only adult to adult transmission

occurs?

Model DevelopmentModel Development

Susceptible Individuals

Infected IndividualsRecruits Natural

Mortality

Natural Disease InducedNatural Mortality

Disease Induced Mortality

Model DevelopmentModel DevelopmentσΨ

A AIAR MNAs AIAR MN

M MMN MD

AR = Recruits AI = Infected MD = Mortality due to diseaseAR RecruitsAS = Susceptible

AI InfectedMN = Natural Mortality

MD Mortality due to diseaseσ = Likelihood of transmissionΨ = Contact Rate

Model DevelopmentModel DevelopmentσΨ·As(t)·AI(t)

A (t) A (t)A (t) M (t)As(t) AI(t)AR(t) MN(t)

M (t) M (t)

AR = Recruits AI = Infected MD = Mortality due to disease

MN(t) MD(t)

AR RecruitsAS = Susceptible

AI InfectedMN = Natural Mortality

MD Mortality due to diseaseσ = Likelihood of transmissionΨ = Contact Rate


Ro = σΨ·As /MN(t)o s N( )

Model DevelopmentModel Development1.00

0.70

0.80

0.90

0.40

0.50

0.60

σ

0.10

0.20

0.30

0.000.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Ψ


• AssumptionsAssumptions– No distinction between ulcerative and hemorrhagic forms of diseasehemorrhagic forms of disease

– Median population size (31 individuals) is accurate(from Teacher et al. 2010)

– The estimated likelihood of transmission from the literature is accurate (calculated from data in Cunningham et al. 2007)2007)

Model UtilityModel Utility

• Can the ranavirus persist in these populationsCan the ranavirus persist in these populations of common frogs if only adult to adult transmission occurs?transmission occurs?– Yes, under certain conditions

• Unlikely to be accurate with the current assumptions– These assumptions need to be verified

Interesting Question 2Interesting Question 2

Can both disease syndromes be maintained in a population?population?

T f f di i i f !– Two forms of disease is unique to common frogs!

Model DevelopmentModel DevelopmentσΨ·As(t)·AU(t)

A)

As(t) AU(t)AR(t) MN(t)

MN(t) MD(t)

σΨ·As(t)·AH(t)B)

A.A. Cunningham

As(t) AH(t)AR(t) MN(t)

MN(t) MD(t)


σ3Ψ·As(t)·AH(t)

AR(t) σ2Ψ·As(t)·AU+H(t)

σ1Ψ·As(t)·AU(t) σ3 Ψ·As(t)·AH(t)

As(t) AU(t) AU+H(t) AH(t)

σ1Ψ·As(t)·AU(t)

MN(t) MD(U)(t) MD(U+H)(t) MD(H)(t)MN(t) MN(t) MN(t)


• New estimates for the likelihood ofNew estimates for the likelihood of transmission are calculated for each syndrome– Ulcerative form: 0 36– Ulcerative form: 0.36

– Hemorrhagic form: 0.44

Thi l t l l t t diff t R• This lets us calculate two different RO



Model UtilityModel Utility

• Can both disease syndromes be maintained inCan both disease syndromes be maintained in a population?– Yes under certain conditions– Yes, under certain conditions…

• Unlikely to be accurate with the current assumptions– These assumptions need to be verified!

Additional Information NeededAdditional Information Needed

• Better estimates of transmission ratesBetter estimates of transmission rates

• Determination of contact rates

i l f di i d d• Experimental assessment of disease induced mortality rates

• Data on pathological progression of disease

• Full characterization of the virus(es)( )

• Wild prevalence data

ConclusionsConclusions

• Models are only as good as the data that areModels are only as good as the data that are used to run them!

• Provide useful guides for future investigations• Provide useful guides for future investigations and experiments.

THANK YOU!THANK YOU!

• Rob Knell ‐ QMULRob Knell QMUL

• Richard Nichols – QMUL

• Trent Garner – IoZQuestions?

Trent Garner IoZ

Funding provided by:• NSERC 3‐Year Doctoral Award

• Queen Mary University of London Research Studentship

• University of London OverseasUniversity of London Overseas Research Studentship

• Department of Biology, Gordon State CollegeState College

Education

Mathematical modeling of ranavirus ecology