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# Mathematical modeling of ranavirus ecology

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2013 International Symposium on Ranaviruses
by Amanda Duffus

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### Mathematical modeling of ranavirus ecology

1. 1. Mathematical Modeling ofMathematical Modeling of  Ranavirus Ecology Dr. Amanda L. J. Duffus Assistant Professor of Biology  Department of Biology Gordon State College, Barnesville, GA aduffus@gordonstate.edu
2. 2. Outline • Potential Role of Disease in Population Declines • Ranaviral Disease in UK Common Frogs • Model Development • Model Utility • Conclusions
3. 3. 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
4. 4. 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
5. 5. Ranaviral Disease in UK Common FrogsRanaviral Disease in UK Common Frogs A A CunninghamA.A. Cunningham
6. 6. Ranaviral Disease in UK Common FrogsRanaviral Disease in UK Common Frogs
7. 7. Ranaviral Disease in UK Common FrogsRanaviral Disease in UK Common Frogs • 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
8. 8. Ranaviral Disease in UK Common FrogsRanaviral Disease in UK Common Frogs • 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)( )
9. 9. Ranaviral Disease in UK Common FrogsRanaviral Disease in UK Common Frogs • 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?
10. 10. 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?
11. 11. Model DevelopmentModel Development Susceptible Individuals Infected Individuals Recruits Natural Mortality Natural Disease InducedNatural Mortality Disease Induced Mortality
12. 12. Model DevelopmentModel Development σΨ A AIAR MNAs AIAR MN M MMN MD AR = Recruits AI = Infected MD = Mortality due to diseaseAR Recruits AS = Susceptible AI Infected MN = Natural Mortality MD Mortality due to disease σ = Likelihood of transmission Ψ = Contact Rate
13. 13. Model DevelopmentModel Development σΨ·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 Recruits AS = Susceptible AI Infected MN = Natural Mortality MD Mortality due to disease σ = Likelihood of transmission Ψ = Contact Rate
14. 14. Model DevelopmentModel Development Ro = σΨ·As /MN(t)o s N( )
15. 15. Model DevelopmentModel Development 1.00 0.70 0.80 0.90 0.40 0.50 0.60 σ 0.10 0.20 0.30 0.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Ψ
16. 16. Model DevelopmentModel Development • 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)
17. 17. 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
18. 18. 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!
19. 19. Model DevelopmentModel Development σΨ·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)
20. 20. Model DevelopmentModel Development 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)
21. 21. Model DevelopmentModel Development • 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
22. 22. Model DevelopmentModel Development
23. 23. Model DevelopmentModel Development
24. 24. 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!
25. 25. 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
26. 26. 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.
27. 27. THANK YOU!THANK YOU! • Rob Knell ‐ QMULRob Knell   QMUL • Richard Nichols – QMUL • Trent Garner – IoZ Questions? 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