Global Dynamics Of Two Planar Parasite-host Models

In this paper we give global dynamical behaviors of a Parasite-host model witha nonlinear incidence rate bxpyq.Firstly,we discuss the global dynamical behaviors inthe case of p = q = 1.In this case,we give the qualitative properties of equilibriain the first quadrant,and study the bifurcations of the system.Particularly,the concretedistribution of orbits near high degenerate equilibrium O are obtained by a methodof generalized normal sectors.Moreover, we consider equilibria at infinity for globaltendency.Lastly, we discuss the qualitative properties of equilibria in the first quadrantin the case of p∈Z+, q = 1,including equilibria at infinity for global tendency.Thus,we get global dynamical behaviors of this Parasite-host model.