Dynamics of Predator-dependent nonlinear disease transmission in infected prey with diverse functional response

Abstract

The disease in prey causes the indirect effect on the disease transmission of prey-predator interactions; this phenomenon of predator-dependent disease transmission scenario can arise as a consequence of anti-predator defence behaviour, debilitating the immune system of the prey.
This concept is implemented in the proposed nonlinear mathematical prey-predator model, where an infectious disease infects only prey populations. The interaction between the susceptible prey and predator is assumed to be governed by Crowley-Martin type functional response and Holling I type functional response for the predation of infected prey. The susceptible prey becomes infected when contact occurs with the infected prey. The existence, uniqueness, boundedness, and feasibility and stability conditions of the fixed points of the system are analyzed. Hopf bifurcation analysis for the system is perceived and presented through bifurcation diagrams for different parameter values. Lastly, numerical exercises and graphical demonstrations are given to help our investigative findings.