Effect On Dynamics Of A Prey-predator Model With Parasite Infection

The size of the population is not only influenced by the species competition and preyed, and are influenced by the parasitic infection, in the control of population dynamics behavior, parasitic plays an important role. In this paper, we investi-gate delayed prey-predator model with parasite infection, and analyze the existence conditions, local stability and global stability of the equilibrium.Firstly, the dynamical behaviors of a prey-predator model with micro parasitic infection in the predator have been discussed. By analyzing the characteristic e-quations, the local asymptotically stability of each of feasible equilibria of system is discussed and existence of a Hopf bifurcation at the internal equilibrium. By using Lyapunov function and LaSalle invariant principle, it is shown that equilibriums are globally asymptotically stable.Secondly, the dynamical behaviors of a prey-predator system with parasitic infection and recover. By analyzing the characteristic equations, the local asymp-totically stability of each of feasible equilibria of system is discussed.Thirdly, the dynamical behaviors of effect of delay on a predator-prey model with parasitic infection have been discussed. By analyzing the basic reproductive number, the local asymptotically stability of each of feasible equilibria of system is discussed. By analyzing the characteristic equations, using Routh-Hurwitz, it is shown that boundary internal equilibrium are local asymptotically stable.