Effects of a disease affecting a predator on the dynamics of a predator-prey system |
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Authors: | Pierre Auger |
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Institution: | a UR GEODES, IRD, Centre de Recherche d’lle de France, 32 av. Henri Varagnat, 93143 Bondy cedex, France b Ecole Nationale de commerce et de Gestion, B.P. 1255, 90000 Tanger, Morocco c Agricultural and Ecological Research Unit, Indian Statistical Institute 203, B.T. Road, Kolkata 700108, India d UR GEODES, IRD and Project-team MASAIE, INRIA Grand-Est, France e UR GEODES, IRD and MAT Laboratory, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon |
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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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Keywords: | Lotka-Volterra model Predator-prey model Infected predators Time scales Aggregation of variables Stability SIRS model |
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