Effects of a disease affecting a predator on the dynamics of a predator-prey system.
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).
Auger
Pierre
P
UR GEODES, IRD, Centre de Recherche d'lle de France, 32 Av. Henri Varagnat, 93143 Bondy Cedex, France.
McHich
Rachid
R
Chowdhury
Tanmay
T
Sallet
Gauthier
G
Tchuente
Maurice
M
Chattopadhyay
Joydev
J
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