A Comparative Study on the Impact of Infection on the Stability of Eco-epidemiological Models

In this research, we formulated and examined a mathematical model to study an infected predator-prey system incorporating two distinct predator functional responses. We established the existence and uniqueness of solutions, demonstrating that they remain uniformly bounded for all initial conditions that are nonnegative. Through a detailed mathematical and biological analysis, we found that when the prey population is impacted by a fatal disease, the coexistence of all three species (host, parasite, and predator) is impossible under either of the two functional responses examined. However, by modulating two crucial factors (the infection rate and the attack rate on susceptible prey) a variety of complex dynamical behaviors can arise. These include transitions in stability, species extinction scenarios, and oscillatory population dynamics.