Stability and Bifurcation Analysis of an Eco-Epidemic Model with Predation-Driven Weak Allee Effect

In this paper, we explore the dynamics of an eco-epidemic model where susceptible prey population is subjected to weak Allee effect, which is also influenced by the predation pressure. We are the first to consider weak Allee effect in the form of predation-driven weak Allee effect in an eco-epidemiological system. We carry out an extensive evaluation, starting with the local stability analysis of equilibrium points and the analysis of transcritical bifurcation, and Hopf bifurcation around the interior equilibrium point. Further, we perform numerical simulations. By our numerical simulations we ensure that the eco-epidemic model exhibits chaos for increasing disease propagation when the effect of weak Allee is absent and the system shows stable solution in the presence of weak Allee effect. We conduct comprehensive numerical experiments and draw one- and two-parameter bifurcation diagrams using numerical continuation software MATCONT to explore more complex dynamics which are not captured analytically.