Mathematical modeling of ranavirus ecology
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Mathematical modeling of ranavirus ecology

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2013 International Symposium on Ranaviruses

2013 International Symposium on Ranaviruses
by Amanda Duffus

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Mathematical modeling of ranavirus ecology Presentation Transcript

  • 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. Outline • Potential Role of Disease in Population Declines • Ranaviral Disease in UK Common Frogs • Model Development • Model Utility • Conclusions
  • 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. 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. Ranaviral Disease in UK Common FrogsRanaviral Disease in UK Common Frogs A A CunninghamA.A. Cunningham
  • 6. Ranaviral Disease in UK Common FrogsRanaviral Disease in UK Common Frogs
  • 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. 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. 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. 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. Model DevelopmentModel Development Susceptible Individuals Infected Individuals Recruits Natural Mortality Natural Disease InducedNatural Mortality Disease Induced Mortality
  • 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. 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. Model DevelopmentModel Development Ro = σΨ·As /MN(t)o s N( )
  • 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. 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. 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. 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. 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. 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. 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. Model DevelopmentModel Development
  • 23. Model DevelopmentModel Development
  • 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. 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. 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. 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