Auger Pierre, McHich R., Chowdhury T., Sallet G., Tchuente M., Chattopadhyay J. (2009). Effects of a disease affecting a predator on the dynamics of a predator-prey system. Journal of Theoretical Biology, 258 (3), p. 344-351. ISSN 0022-5193.
Titre du document
Effects of a disease affecting a predator on the dynamics of a predator-prey system
Auger Pierre, McHich R., Chowdhury T., Sallet G., Tchuente M., Chattopadhyay J.
Source
Journal of Theoretical Biology, 2009,
258 (3), p. 344-351 ISSN 0022-5193
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).
Plan de classement
Sciences fondamentales / Techniques d'analyse et de recherche [020]
