# Uniform persistence in a prey-predator model with a diseased predator

## TL;DR

This paper provides a rigorous mathematical analysis of a prey-predator model with a diseased predator, explaining conditions for persistence and stability, and offering insights into disease invasion dynamics.

## Contribution

It introduces a novel theoretical framework for analyzing disease effects in prey-predator models using persistence theory and stability analysis.

## Key findings

- Conditions for disease invasion are derived.
- The model demonstrates uniform persistence under certain parameters.
- Stability analysis reveals the impact of disease on predator-prey dynamics.

## Abstract

Following the well-extablished mathematical approach to persistence and its recent developments we give a rigorous theoretical explanation to the numerical results obtained for a certain prey-predator model with functional response of Holling type II equipped with an infectious disease in the predator population. The proof relies on some repelling conditions that can be applied in an iterative way on a suitable decomposition of the boundary. A full stability analysis is developed, showing how the "invasion condition" for the disease is derived. Some counterexamples and possible further investigations are discussed.