Travelling Waves Of Two Kinds Of Nonlocal Dispersal SIR Epidemic Model

In this thesis, we consider the existence and nonexistence of traveling wave solutions of two kinds of nonlocal dispersal SIR epidemic model. The main result is divided into two chapters.In the second chapter, we consider a nonlocal dispersal SIR epidemic model. We find that the existence and nonexistence of traveling wave solutions are deter-mined by the reproduction number. To prove the existence of non-trivial traveling wave solutions, we construct an invariant cone in a bounded domain with initial functions being defined on, and apply Schauder’s fixed point theorem on this cone, then pass to the unbounded domain by a limiting argument. By means of the two-sided Laplace transform, the nonexistence of traveling wave solutions is obtained as the speed is less than the critical velocity.In the third chapter, we use the same method as the second chapter to study the existence and nonexistence of traveling wave solutions of a delayed nonlocal dispersal SIR epidemic model with constant external suplies and Holling-Ⅱ incidence rate.