# Bifurcation and hybrid control of a discrete eco-epidemiological model with Holling type-III

## TL;DR

This paper studies a discrete eco-epidemiological model and analyzes its bifurcations and control strategies.

## Contribution

The novel contribution is the hybrid control strategy for managing bifurcations in the model.

## Key findings

- The system exhibits Neimark-Sacker and flip bifurcations at the positive fixed point.
- A hybrid control strategy successfully manages the Neimark-Sacker bifurcation.
- Numerical simulations confirm the analytical results.

## Abstract

In this paper, a three dimensional discrete eco-epidemiological model with Holling type-III functional response is proposed. Boundedness of the solutions of the system is analyzed. Existence condition and stability of all fixed points are discussed for the proposed model. Furthermore, we obtained the transcritical bifurcation surfaces of the system by bifurcation theory. Based on the explicit criteria for the Neimark Sacker bifurcation and flip bifurcation, we obtained that the system undergoes these two types of bifurcations at the positive fixed point. Then we apply a hybrid control strategy that based on both parameter perturbation and a state feedback strategy to control the Neimark-Sacker bifurcation. Finally, some numerical simulations are carried out to support the analytical results.