Dynamic Behavior Of A Host-Macroparasite Diffusion Model

In this paper,the stability,Hopf bifurcation and diffusion-driven Turing insta-bility of a host-macroparasite diffusion model are investigated.First,we discuss the stability of nonnegative equilibria and the existence,the direction and stability of Hopf bifurcation for the corresponding ODE model.Then,we give the conditions of Turing instability for the reaction-diffusion model by linearization analysis,and discuss the existence and direction of Hopf bifurcation and the stability of the bi-furcating periodic solutions.Moreover by choosing suitable parameters and using Matlab software,numerical simulations are performed to verify and supplement the results of theoretical analysis.