A seasonal SIR metapopulation model with an Allee effect with application to controlling plague in prairie dog colonies

For wildlife species living among patchy habitats, disease and the Allee effect (reduced per capita birth rates at low population densities) may together drive a patch's population to extinction, particularly if births are seasonal. Yet local extinction may not be indicative of global extinctio...

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Bibliographic Details
Published in:Journal of biological dynamics 2015-06, Vol.9 (sup1), p.262-290
Main Authors: Ekanayake, A.J., Ekanayake, D.B.
Format: Article
Language:English
Subjects:
Allee effect
Animal diseases
Animals
Birth
Colonies
Computer Simulation
Disease
Disease Susceptibility
Dispersal
Endangered & extinct species
Epidemic models
Eradication
Extinction
Immunization
Metapopulations
Models, Biological
Numerical Analysis, Computer-Assisted
periodic solutions
Plague
Plague - epidemiology
Plague - prevention & control
Plague - transmission
Plague - veterinary
Population Density
Population Dynamics
Prairie dogs
Sciuridae - microbiology
Seasons
Species extinction
stochastic epidemic model
Stochasticity
Sylvatic plague
Time Factors
vector control
Wildlife
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Summary:For wildlife species living among patchy habitats, disease and the Allee effect (reduced per capita birth rates at low population densities) may together drive a patch's population to extinction, particularly if births are seasonal. Yet local extinction may not be indicative of global extinction, and a patch may become recolonized by migrating individuals. We introduce deterministic and stochastic susceptible, infectious, and immune epidemic models with vector species to study disease in a metapopulation with an Allee effect and seasonal birth and dispersal. We obtain conditions for the existence of a strong Allee effect and existence and stability of a disease-free positive periodic solution. These general models have application to many wildlife diseases. As a case study, we apply them to evaluate dynamics of the sylvatic plague in prairie dog colonies interconnected through dispersal. We further evaluate the effects of control of the vector population and control by immunization on plague eradication.
ISSN:1751-3758
1751-3766
DOI:10.1080/17513758.2014.978400