Dynamical Analysis of a Three-Species Diseased Food Web Model with Different Functional Responses

This paper presents a three-species diseased food web dynamical model that relies on interactions between species of susceptible (healthy) prey, infectious (diseased) prey, and predators. It is suggested that in the absence of predator species, the prey population grows logistically. Predators are assumed to consume their prey in the form of Beddington-DeAngelis and Crowley-Martin response function. In addition, diseased prey is hypothesized to consume healthy prey using the Holling type II functional response. This dynamical model is examined in terms of positivity, boundedness, and positivity invariance. Furthermore, we explored every biologically feasible equilibrium point in the system. Also, the local stability of non–negative equilibria and the global stability are evaluated by suitable Lyapunov functions. Moreover, the Hopf bifurcation has undergone analysis at the infection rate. Finally, numerical solutions are investigated in accordance with our findings.