Dynamics of a discrete eco-epidemiological model with disease in the prey

TL;DR

This paper develops a discrete eco-epidemiological model incorporating disease dynamics in prey, analyzing conditions for persistence and extinction of infected prey using nonstandard numerical methods.

Contribution

It introduces a novel discrete model for eco-epidemiology with general predation functions and provides analysis on infected prey persistence and extinction.

Findings

Conditions for infected prey persistence and extinction

Use of Mickens nonstandard method for model discretization

Illustrative examples and simulations confirming theoretical results

Abstract

Using Mickens nonstandard method, we obtain a discrete family of nonautonomous eco-epidemiological models that include general functions corresponding to the predation of the infected and uninfected preys. We obtain results on the persistence and extinction of the infected preys assuming that the bi-dimensional predator-prey subsystem that describes the dynamics in the absence of the infection satisfies some assumptions. Some examples and simulations are undertaken to illustrate our results.