The Dynamics Of SEIS Epidemic Model With Diffusion Terms

When we study the epidemic model,considered the flowing of the populations,we do not neglect the spatial dispersal of epidemics.So by the addition of diffusion terms and initial-boundary value to the ordinary differential SEIS epidemic model,we study the corresponding diffusion model systematically.In this lecture,we mainly study the dynamics of the SEIS model on the boundary conditions of Dirichlet and Neumann, specifically study the structure and related properties of the equilibriums.We get some practical conclusions .They provide a more reliable theory bases for revealing the epidemic laws and formulating the epidemic preventions.There are four chapters in this thesis.In Chapter 1, we briefly introduce the significance of studying the epidemic dy-namics,and bring in the SEIS epidemic model with diffusion terms.In Chapter 2, we study the dynamics of SEIS model on the boundary condition of Dirichlet.Firstly,introduce the theory and method of the fixed point index in mapping cone ,secondly,study the equilibriums' existence of the system by them.In Chapter 3, according to the eigenvalue problem of the system,we judge the local stability of the constant equilibrium by the eigenvalue.In Chapter 4, the main conclusions of this thesis are summarized, and the further research significance are presented at last.