Study On Two Kinds Of SIS Reaction Diffusion Model

This paper mainly studies two problems.The first one proposes and studies a simpli-fied SIS model to understand the impact of the spatial heterogeneity of environment and convection on the persistence and eradication of infectious diseases.The free boundary is introduced to simulate the front of disease propagation.The basic reproduction quantity related to diseases in space environment is introduced.Sufficient conditions are given to eradicate or spread the disease.Our results show that if the spread area is at high risk at a certain time,the disease will continue to spread until the whole area is infected.If the spread domain is low-risk,the disease may disappear or continue to spread,depending on the expansion ability of infection ability and the initial number of peopleIn the second model,we will study an improved SIS diffusion model with Dirichlet boundary conditions,which reflect the hostile environment in the boundary.The basic reproduction number is defined,which plays a crucial role in determining whether the disease will become extinct or persist.We have shown that when the basic reproductive number is less than 1,the disease will disappear,and when the basic reproductive number exceeds 1,the epidemic balance will be reached.Part of the results of the overall stability of the local equilibrium were also obtained.