A Discrete Predator-Prey Ecoepidemic Model

¹ U.D. Matemáticas, Universidad de Alcalá, 28871 Alcalá de Henares, Spain
² Dpto. Matemática Aplicada, ETSI Industriales, Univ. Politécnica de Madrid, 28006 Madrid, Spain

^* Corresponding author. E-mail: rafael.bravo@uah.es

Abstract

In this work we present a discrete predator-prey ecoepidemic model. The predator-prey interactions are represented by a discrete Leslie-Gower model with prey intra-specific competition. The disease dynamics follows a discrete SIS epidemic model with frequency-dependent transmission. We focus on the case of disease only affecting prey though the case of a parasite of the predators is also presented. We assume that parasites provoke density- and trait-mediated indirect interactions in the predator-prey community that occur on a shorter time scale. This is included in the model considering that in each time unit there exist a number k of episodes of epidemic changes followed by a single episode of demographic change, all of them occurring separately. The aim of this work is examining the effects of parasites on the long-term prey-predators interactions. These interactions in the absence of disease are governed by the Leslie-Gower model. In the case of endemic disease they can be analyzed through a reduced predator-prey model which summarizes the disease dynamics in its parameters. Conditions for the disease to drive extinct the whole community are obtained. When the community keeps stabilized different cases of the influence of disease on populations sizes are presented.