Hopf bifurcation in an eco-epidemic model

This paper deals with prey-predator system where the prey population is infected with a microparasite. Predator functional response is assumed to be Holling type I. All the feasible equilibrium points of the system are obtained and the condition for the existence of positive (interior) equilibrium point is also determined. The criteria for both local stability and instability involving system parameters are derived. The criterion for existence of Hopf-type small periodic oscillation is shown. The condition for survival of all the population is investigated. We have developed a necessary and sufficient criteria for uniform persistence. Finally, the numerical verifications of analytic results are done.