Traveling Wave Solution For Two Classes Of Diffusive Epidemic Models

In this paper,two diffusive models are discussed.By simplified shooting method and shooting method,the existence of traveling wave solution are proved and the minimal wave speed is obtained.These results provide a theoretical basis for the spread of the infectious diseases.The first chapter is devoted into the introduction on the background of models,mathematical methods and conclusions.In chapter 2,we study a class of diffusive epidemic system under the condition that the infectious have the capacity to diffuse.Then,the SIR system is decouped for SI system.By using Routh-Hurwitz criterion,we investigate the local stability of equilibrium points.At the same time,we prove the existence of the traveling wave solution with the help of the simplified shooting method and Liapunov function.In chapter 3,we explore a class of diffusive epidemic system under the condition that the infectious and the susceptible have the same capacity to diffuse.First,we establish the sufficient condition about the nonexistence of traveling wave solutions.Next,we use shooting method to construct a E set and find the global positive solution in the E set.Then we use the Liapunov function method to prove that the global positive solution converges to the local disease equilibrium when t? +?,that is,traveling wave solution exists.