Bifurcation and global stability in an eco-epidemic model with refuge

Abstract

In this work, we formulate a predator–prey–pathogen model in which the predator is specialist in nature and infected prey can undergo refugia of constant size to avoid predator attack. To investigate the predation effect on the epidemics, we take a situation where the predator eats infected prey only. This is in accordance with the fact that the infected individuals are less active and can be caught more easily. Though it is a well-known fact that consumption of infected prey may harm predator population, the opposite holds in few cases. This leads to a controlled measure of disease prevalence. As predator consumes a particular type of prey species, Holling type II functional response is appropriate. This corroborates to the specialist type of predator. For biological validity of the model, boundedness of the system is studied. The dynamical behavior of the model has been analyzed throughly. Model analysis shows that all the population remains in coexistence when predator consumes the infected prey rather than the susceptible one. The results establish the fact that the effects of refuge used by prey decrease the equilibrium density of susceptible prey population, whereas the opposite holds for infected prey population. However, equilibrium density of predator may decrease or increase by increasing the amount of prey refuge. Global stability of the coexistence equilibrium point is developed by using Li and Muldowney’s high-dimensional Bendixson’s criterion. Numerical simulations are performed to validate our theoretical results.