Traveling Waves Of DS-DI Epidemic Model

This thesis is concerned with the existence and nonexistence of nontrivial trav-eling wave solutions of DS—DI epidemic model. The thesis consists of the following two chapters.In chapter1, we introduce the background of the epidemic and some related knowledge. Firstly, we state the epidemic is harmful to human healthy and it is meaningful for researching the epidemic. Secondly, we introduce the development of the epidemic mathematical model and the main results of the thesis. That is we consider a nonlocal delay DS—DI epidemic model, and find that the existence and nonexistence of traveling wave solutions are determined by the reproduction number R0.In chapter2, we prove the main results of this thesis. When R0>1, we con-struct an invariant cone of initial functions defined in a bounded domain, and apply a fixed point theorem on this cone, then extend to the unbounded domain R by a limiting argument. When R0<1, we prove the nonexistence of traveling wave solutions by a contradiction argument.