Traveling Wave Solutions For Two Diffusive Epidemic Models

Two diffusive epidemic models with susceptible,asymptomatically infected,symptomat-ically infected and vaccinated(SAIV)individuals are considered.The existence of traveling wave solutions of these models indicates that under what conditions can an epidemic can the study of existence of traveling wave solutions of epidemic models can help people to prevent and take measures to control the epidemics in advance.The first part studies a diffusive SAIV epidemic model with time delay.A perturbed system of the corresponding traveling wave system is introduced.The existence of a solution to this perturbed system is obtained by the method of upper and lower solutions together with Schauder's fixed point theorem.Some properties of this solution are also presented.The ex-istence of a super-critical traveling wave solution is obtained by the approximation method.The positiveness of the super-critical traveling wave solution is derived by the expression of the operator and the lower solutions.The asymptotic boundary of the super-critical travel-ing wave solution are found by the squeezing method and some important properties of the solution.At last,the existence of a non-trivial,positive and bounded critical traveling wave solution is derived by the limiting approach together with dominated convergence theorem and the strong maximum principle.The second part is concerned with a mixed diffusion SAIV epidemic mode.A perturbed system of the corresponding traveling wave system is introduced.The solution of this per-turbed system is obtained by combing the method of upper and lower solutions and Schauder's fixed point theorem.Then the positiveness and asymptotic boundary of this solution are de-rived by delicate analysis.The existence of a super-critical traveling wave solution is estab-lished by the uniform boundedness of the solution with the auxiliary function method and approximation method.Finally,the existence of a non-trivial,positive and bounded critical traveling wave solution is obtained by the limiting approach together dominated convergence theorem and the strong maximum principle.