%0 Journal Article
%9 ACL : Articles dans des revues avec comité de lecture répertoriées par l'AERES
%A Auger, Pierre
%A McHich, R.
%A Chowdhury, T.
%A Sallet, G.
%A Tchuente, M.
%A Chattopadhyay, J.
%T Effects of a disease affecting a predator on the dynamics of a predator-prey system
%D 2009
%L fdi:010046096
%G ENG
%J Journal of Theoretical Biology
%@ 0022-5193
%K Lotka-Volterra model ; Predator-prey model ; Infected predators ; Time scales ; Aggregation of variables ; Stability ; SIRS model
%M ISI:000266120200003
%N 3
%P 344-351
%R 10.1016/j.jtbi.2008.10.030
%U https://www.documentation.ird.fr/hor/fdi:010046096
%> https://www.documentation.ird.fr/intranet/publi/2009/06/010046096.pdf
%V 258
%W Horizon (IRD)
%X 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).
%$ 020