The impact factors of the risk index and diffusive dynamics of a SIS free boundary model()

To discuss the impact factors on the spread of infectious diseases, we study a free boundary problem describing a SIS (susceptible-infected-susceptible) model in a heterogeneous environment. Firstly, the existence and uniqueness of the global solution are given. Then the basic reproduction number related to time is defined, and a spreading-vanishing dichotomy of infectious diseases is obtained. The impacts of the diffusion rate of infected individuals, expanding capability, and the scope and scale of initial infection on the spreading and vanishing of infectious disease are analyzed. Numerical simulations are given to show that the large expanding capability is unfavorable to the prevention and control of the disease.