title: 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).
authors.affiliation: UR GEODES, IRD, Centre de Recherche d'lle de France, 32 Av. Henri Varagnat, 93143 Bondy Cedex, France.
authors.forename: Pierre
authors.initials: P
authors.lastname: Auger
authors.forename: Rachid
authors.initials: R
authors.lastname: McHich
authors.forename: Tanmay
authors.initials: T
authors.lastname: Chowdhury
authors.forename: Gauthier
authors.initials: G
authors.lastname: Sallet
authors.forename: Maurice
authors.initials: M
authors.lastname: Tchuente
authors.forename: Joydev
authors.initials: J
authors.lastname: Chattopadhyay
mesh_terms: D000820:Animal Diseases; D000818:Animals; D003198:Computer Simulation; D017753:Ecosystem; D020387:Food Chain; D005716:Game Theory; D008954:Models, Biological; D011156:Population Density; D011235:Predatory Behavior