Local Bifurcation and Global Stability of an Eco‐Epidemiological Model Incorporating Fear Effect and Prey Harvesting

In ecological point of view, fears from predator may reduce the reproduction of prey and harvesting and intraspecific competition among predators, may changes the behavior of dynamical interaction between predator and their prey. In this paper, a Holling Type II prey–predator model with SI ‐type of disease in prey has been modified and analyzed. Firstly, some properties like positivity and boundedness of the solutions of the model are proved and then the criterion that makes the model equilibrium points persist is determined. The criterion for locally as well as globally asymptotically stable of the each model is investigated. The application of the hypothesis of the Sotomayor theorem for local bifurcation near the equilibrium points is adopted. Finally, further investigations for the global dynamics and confirmation the analytical results of the system are carried out with the help of numerical simulations. It is observed that both fear and harvesting rate may cause extinction in the predator.