Dynamical Behavior of a Predator-Prey Model Involving Disease Spread, Predator Cannibalism, and Harvesting

This paper is concerned with a model of disease transmission in predator-prey, predator cannibalism, and harvesting. We demonstrate that the model’s solution is bounded and positive. Then, we investigate each potential equilibrium point’s existence and stability. The local stability of the model around each equilibrium point is studied by the linearizing the system using Jacobian Matrix, while the global stability is performed by defining a Lyapunov function. The model has six equilibria, which are conditionally locally asymptotically stable. Global stability analysis performed shows that all equilibria are conditionally globally asymptotically stable. To support our analytical findings, we also perform numerical simulations.