A predator-prey model with disease in the prey

Chattopadhyay, J. ; Arino, O. (1999) A predator-prey model with disease in the prey Nonlinear Analysis, 36 . pp. 747-766.

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After the seminal models of Vito Volterra and Alfred James Lotka in the mid 1920s for predator-prey interactions, mutualist and competitive mechanisms have been studied extensively in the recent years by researchers. There are so many references in this context, we have just cited here some books (e.g. see, [14, 16{18, ?] and the refer- ences therein). Similarly, after the pioneering work of Kermack{McKendrick on SIRS (susceptible-infective-removal-susceptible) epidemiological models have also received much attention from scientists. Relevant references in this context are also vast and we shall again mention here some books (see [1, 2, 4], to mention a few). But little attention has been paid so far to merge these two important areas of research (see [7, 21]). In this paper, we shall put emphasis in such an eco-epidemiological system. We consider a three species eco-epidemiological system, namely, sound prey (suscep- tible), infected prey (infective) and predator. We consider the case when the predator mainly eats the infected prey. This is in accordance with a previous model by Hadeler and Freedman [7] which describes a predator-prey model where the prey is infected by a parasite, and the prey in turn infects the predator with that parasite. The infec- tion weakens the prey and increases its susceptibility to predation, while no predator impairing elect is accounted for. While the paper is mainly theoretical and does not address any specific situation, the reader may and several examples in [7]. We derive persistence and extinction conditions of the populations and we also determine conditions for which the system enters a Hopf-type bifurcation. Moreover, we observe that the bifurcated branches are supercritical in some parametric region space in a special case when the predator response function is a Holling-type II function.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Sound Prey; Infected Prey; Predator; Hopf Bifurcation; Poincare Map
ID Code:7560
Deposited On:25 Oct 2010 11:13
Last Modified:16 May 2016 17:44

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