A predator–prey model with disease in the predator species only

In this paper we propose a predator–prey model with logistic growth in the prey population that includes an SIS parasitic infection in the predator population, with the assumption that the predator has an alternative source of food. For simplicity we initially work with a model involving the fractions of the predator which are susceptible and those infected and then translate the results back to the model with absolute numbers. Important thresholds R1,R2, R3 and R4 are identified and their implications have been explained. Our theoretical study indicates that the absence of prey may be beneficial for predator when a transmissible disease runs among the predator population. One important conclusion is that infection in the predator species may save the prey from extinction even if , the basic reproduction number for the prey to be able to invade the predator-only equilibrium, is less than one. Therefore infection in the predator species may be taken as biological control. Finally, analytical results have been supported by numerical simulations with the help of experimental data.