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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).
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https://hal.inria.fr/hal-00764623
Contributor : Gauthier Sallet <>
Submitted on : Thursday, December 13, 2012 - 11:31:44 AM
Last modification on : Wednesday, June 2, 2021 - 9:36:45 AM

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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, Elsevier, 2009, 258 (3), pp.344-351. ⟨10.1016/j.jtbi.2008.10.030⟩. ⟨hal-00764623⟩

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