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

Abstract

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.