Role of infection on the stability of a predator–prey system with several response functions—A comparative study

In this paper, we have proposed and analyzed a mathematical model of an infected predator–prey system with different predators’ functional response. The existence and uniqueness of solutions are established and solutions are shown to be uniformly bounded for all nonnegative initial values. Our overall mathematical and biological studies reveal that if the prey population is infected by a lethal disease, coexistence of all three species (i.e. host, parasite and predator) for any of three functional responses is never possible but different interesting dynamical behaviors are possible by varying two key parameters viz. the rate of infection and the attack rate on susceptible prey. Interplay between these two factors yields a diverse array of biologically relevant behavior, including switching of stability, extinction and oscillations.