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  • Title: Effects of a disease affecting a predator on the dynamics of a predator-prey system.
    Author: Auger P, McHich R, Chowdhury T, Sallet G, Tchuente M, Chattopadhyay J.
    Journal: J Theor Biol; 2009 Jun 07; 258(3):344-51. PubMed ID: 19063903.
    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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