Stability Analysis of Prey-Predator Model with Infection, Migration and Vaccination in Prey

A four dimensional ecoepidemiological model consisting of susceptible prey, infected prey, vaccinated prey and predator is formulated and analyzed in the present work. The functional response is assumed to be of Lotka-Volterra type. We studied systematically the behavior of the model with and without disease in prey. We analyzed mathematically the dynamics of the system such as boundedness of the solutions, existence and stability conditions of equilibria. The basic reproduction number \mathcal{R}_0 for the proposed model is computed. Disease is endemic if \mathcal{R}_0>1. Numerical simulations are also carried out for the analytical results.