DYNAMICS AND BIFURCATION ANALYSIS OF AN ECO-EPIDEMIOLOGICAL MODEL IN CROWLEY-MARTIN FUNCTIONAL RESPONSE WITH THE IMPACT OF FEAR

This article consists of a three-species food web model that has been developed by considering the interaction between susceptible prey, infected prey, and predator species. It is assumed that susceptible prey species grow logistically in the absence of predators. It is assumed that predators consume susceptible and infected prey and infected prey consumes susceptible prey. We consider the effect of fear on susceptible prey due to infected prey species. Furthermore, the predator consumes its prey in the form of Holling-type and Crowley-Martin-type interactions. Also, infected prey consumes susceptible prey in the form of Holling-type interaction. The positive invariance, positivity, and boundedness of the system are discussed. The conditions of all biologically feasible equilibrium points have been examined. The local stability of the systems around these equilibrium points is investigated and global stability is analyzed by suitable Lyapunov functions around these equilibrium points. Furthermore, the occurrence of Hopf-bifurcation concerning harvesting (h) of the system has been investigated. Finally, we demonstrate some numerical simulation results to illustrate our main analytical findings.