The diffusive eco-epidemiological prey-predator model with infectious diseases in prey

TL;DR

This paper analyzes a diffusive eco-epidemiological prey-predator model with infectious prey, establishing stability conditions and the absence of pattern formations under different boundary conditions.

Contribution

It provides a comprehensive stability analysis of the model under Neumann and Dirichlet boundary conditions, including existence and uniqueness of positive equilibria.

Findings

No periodic solutions or Turing patterns under Neumann conditions.

Conditions for existence of positive equilibria under Dirichlet conditions.

Global stability results for trivial and semi-trivial equilibria.

Abstract

This paper focus on the diffusive eco-epidemiological prey-predator model with infectious diseases in prey, and with the homogeneous Neumann and Dirichlet boundary conditions, respectively. When boundary conditions are homogeneous Neumann boundary conditions, we give a complete conclusion about the stabilities of nonnegative constant equilibrium solutions. The results show that such a problem has neither periodic solutions nor Turing patterns. When boundary conditions are homogeneous Dirichlet boundary conditions, we first establish the necessary and sufficient conditions for the existence of positive equilibrium solutions, and prove that the positive equilibrium solution is unique when it exists. Then we study the global asymptotic stabilities of trivial and semi-trivial nonnegative equilibrium solutions.