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Stability and Hopf bifurcation in delayed Eco-epidemiological model for nonlinear incidence

Ning Chen, Baodan Tian, Jiqian Chen

In this paper, a delayed eco-epidem iological model with nonlinear incidence is considered Firstly, the sufficient conditions of local stability of the positive equilibrium arc given by analyzing the linearized system characteristic value. Furthermore, conditions ensuring the existence of Hopf bifurcation are obtained. Then, based on centermanifold and normal form, we get the formulas for determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions. At last, some numerical simulations are carried out to support the analytical results.