A Predator-prey Model With Transition Two Infectious Diseases in Prey and Harvesting of The Predator

Abstract

In this paper, we proposed and study prey-predator model involving effect of transition different infectious diseases in prey population with the optimal harvesting for metapopulation, especially predator population, using dynamics programming. Sufficient conditions on the system parameters are derived which guarantee that the equilibrium points of the system are globally asymptotically stable while the harvesting which has an effect on the stability of this system satisfies certain conditions. Also, we discuss the existence of local bifurcation at each equilibrium point. Finally the effects both of the disease and harvest on the dynamical behavior the model are discussed numerically.

Keywords: SIS epidemics disease, Predator-prey model, Harvest management; Global stability; Lyaponov function; local bifurcation.