Global stability and Hopf bifurcation of a delayed eco-epidemiological model with Holling type II functional response.

In this paper, a delayed eco-epidemiological model with Holling type II functional response is investigated. By analyzing corresponding characteristic equations, the local stability of each of the feasible equilibria and the existence of Hopf bifurcations at the disease-free equilibrium, the susceptible predator-free equilibrium and the endemic-coexistence equilibrium are established, respectively. By means of Lyapunov functionals and LaSalle's invariance principle, sufficient conditions are derived for the global stability of the endemic-coexistence equilibrium, the disease-free equilibrium, the susceptible predator-free equilibrium and the predator-extinction equilibrium of the system, respectively. Numerical simulations are carried out to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]