Stability Analysis of Prey-Predator Model with Infection, Migration and Vaccination in Prey

TL;DR

This paper develops and analyzes a four-dimensional ecoepidemiological prey-predator model incorporating infection, vaccination, and migration, providing insights into disease dynamics and stability conditions.

Contribution

It introduces a novel prey-predator model with infection and vaccination, analyzing stability and disease persistence with mathematical and numerical methods.

Findings

Disease is endemic if R0 > 1

Model solutions are bounded and stable under certain conditions

Numerical simulations support analytical results

Abstract

A four dimensional ecoepidemiological model consisting of susceptible prey, infected prey, vaccinated prey and predator is formulated and analyzed in the present work. The functional response is assumed to be of Lotka-Volterra type. We studied systematically the behavior of the model with and without disease in prey. We analyzed mathematically the dynamics of the system such as boundedness of the solutions, existence and stability conditions of equilibria. The basic reproduction number \mathcal{R}_0 for the proposed model is computed. Disease is endemic if \mathcal{R}_0>1. Numerical simulations are also carried out for the analytical results.