S. I. S Model for Disease Transmission from Prey to Predator

Abstract

A model for disease transmission in a predator-prey system has been proposed and analyzed in this paper. From infected prey, the disease is spreading to susceptible prey and consequently to predator species. The disease does not cause immunity in the prey and predator species. Therefore, SIS (Susceptible-Infected-Susceptible) models are considered for both the species. Conditions for the existence and stability of disease free prey predator system are obtained. The next generation approach is used to obtain the epidemiological threshold quantities 0 R , 1 R for the model system. Conditions for endemic disease in prey species are discussed. The predator may become extinct due to disease in prey. Disease is not found to be endemic in both the prey and predator species.