The Effect of Fear and Refuge on the Dynamics of a Predator–Prey Model Incorporating Disease in Predator

Considering the importance of ecosystems from an economic and biological point of view, a new ecological model consisting of prey and a predator with an infectious disease in the presence of fear of predation and refuge has been proposed and studied. The research is aimed at studying these factors’ influence on the predator–prey system’s dynamic behavior in the presence of infectious diseases. The system’s solution properties and limitations were studied. All the necessary conditions for the system’s stability locally and globally are calculated using various mathematical methods. The possibility of local bifurcation in the system has been studied. Finally, the system was solved numerically to confirm the results and understand the effect of changing parameter values on dynamic behavior. It has been found that, up to a critical value, the system is stabilized by the fear of susceptible predators; beyond that, predator extinction threatens the system. A similar observation has been made regarding the refuge rate. Nonetheless, the system dynamics are destabilized by the fear of the infected predators.