2013 International Symposium on Ranaviruses by Amanda Duffus

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