The biological system relies heavily on the interaction between prey and predator. Infections may spread from prey to predators or vice versa. This study proposes a virus-controlled prey-predator system with a Crowley–Martin functional response in the prey and an SI-type in the prey. A prey-predator model in which the predator uses both susceptible and sick prey is used to investigate the influence of harvesting parameters on the formation of dynamical fluctuations and stability at the interior equilibrium point. In the analytical section, we outlined the current circumstances for all possible equilibria. The stability of the system has also been explored, and the required conditions for the model’s stability at the equilibrium point have been found. In addition, we give numerical verification for our analytical findings with the help of graphical illustrations.

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.