Dynamics of an eco-epidemiological system: Predators get infected in two paths

Dealing with the prey-predator interactions in presence of disease is very important to understanding the dynamical behavior of population models. Here, we examine an eco-epidemiological model, in which both populations are infected. The predator population becomes infected by consuming infected prey. Once the predator population gets infected through the infected prey, it is likely susceptible predators can be infected through intraspecific contact with the infected predator even if the infected prey dies out from the system. Mathematically, we have analyzed the stability of all possible equilibria. Moreover, threshold values of the model parameters are obtained for which the system exhibits Hopf, transcritical, and saddle node bifurcations. Numerical simulations are used to verify the accuracy of the analysis. Furthermore, a global sensitivity analysis is performed in MATLAB to find the sensitive model parameters with infected populations. Complex dynamics such as chaos, bistability, and oscillatory coexistence of different periods are observed in the proposed system. We numerically verify the stability of the equilibrium points.