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

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• 作者：Pierre Auger ; Rachid Mchich ; Tanmay Chowdhury ; Gauthier Sallet ; Maurice Tchuente ; Joydev Chattopadhyay
• 关键词：Lotka– ; Volterra model ; Predator– ; prey model ; Infected predators ; Time scales ; Aggregation of variables ; Stability ; SIRS model
• 刊名：Journal of Theoretical Biology
• 出版年：2009
• 出版时间：7 June 2009
• 年：2009
• 卷：258
• 期：3
• 页码：344-351
• 全文大小：641 K

文摘

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).