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Journal Articles Journal of Theoretical Biology Year : 2009

Effects of a disease affecting a predator on the dynamics of a predator-prey system

Abstract

We study the effects of a disease affecting a predator on the dynamics of a predator-prey system. We couple an SIRS model applied to the predator population, to a Lotka-Volterra model. The SIRS model describes the spread of the disease in a predator population subdivided into susceptible, infected and removed individuals. The Lotka-Volterra model describes the predator-prey interactions. We consider two time scales, a fast one for the disease and a comparatively slow one for predator-prey interactions and for predator mortality. We use the classical "aggregation method" in order to obtain a reduced equivalent model. We show that there are two possible asymptotic behaviors: either the predator population dies out and the prey tends to its carrying capacity, or the predator and prey coexist. In this latter case, the predator population tends either to a "disease-free" or to a "disease-endemic" state. Moreover, the total predator density in the disease-endemic state is greater than the predator density in the "disease-free" equilibrium (DFE).

Dates and versions

hal-00764623 , version 1 (13-12-2012)

Identifiers

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Pierre Auger, Rachid Mchich, Tanmay Chowdhury, Gauthier Sallet, Maurice Tchuente, et al.. Effects of a disease affecting a predator on the dynamics of a predator-prey system. Journal of Theoretical Biology, 2009, 258 (3), pp.344-351. ⟨10.1016/j.jtbi.2008.10.030⟩. ⟨hal-00764623⟩
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