On the dynamics of evolutionary Leslie-Gower predator-prey eco-epidemiological model with disease in predator

Abstract In this paper, a Leslie-Gower predator-prey model with disease in the predator has been developed. Lesli-Gower model can be treated as an evolutionary version of Lotka-Volterra model as a result of the genetic consequences. The total population has been divided into three classes, namely, prey, susceptible predator and infected predator. We have studied the positivity and boundedness of the solutions of the system. The local and global dynamical behaviours together with sufficient conditions for persistence of the ecosystem near biologically feasible equilibria are thoroughly investigated. The conditions, which guarantee the occurrence of Hopf-bifurcation of the system, are established. Numerical simulations have been performed to validate the analytical results.