Traveling Waves Of A Class Of Nonlocal Dispersal Models

This thesis is concerned with the existence and nonexistence of traveling wave solutions of a class of nonlocal dispersal epidemic models.First, we introduce the background of the epidemic models and a dispersal influenza model with treatment as well as the main work of the thesis.Second, we consider the existence of traveling wave solutions of nonlocal dis-persal influenza model with treatment. We introduce a auxiliary system with a parameter ε and construct an invariant cone on a bounded region to prove the ex-istence of traveling wave solutions when R0>1. Then we prove that there exists a fixed point on this cone by using Schauder Fixed Point Theory, and show the existence of traveling wave solutions of the primary model by a limiting argument to the auxiliary system.Finally, we consider the nonexistence of traveling wave solutions of nonlocal dispersal influenza model with treatment. When B0>1, we obtain the nonexistence of traveling wave solutions as the speed is less then the given velocity by using Two-sided Laplace transform, while for R0<1 and any c>0, we get the nonexistence of traveling wave solutions by using Fubini’s theory and a contradiction argument.