Traveling Wave Solutions For A Nonlocal Dispersal SEIR Epidemic Model

It is well know that the diffusion terms of classical reaction diffusion equations are described by Laplace operators.However,Laplace operators only reflect local interactions in space.Actually,species move in a wide expance of space not only in a small area in the biological population,which leads to the effect of nonlocal dispersal.Therefore,it is more meaningful and valuable in theory and practice to study the nonlocal dispersal equations.In this thesis,we consider a nonlocal dispersal SEIR epidemic model with saturating incidence rate and constant external suplies.Firstly,the well posedness of the model is obtained via the Banach contracting theorem.Then the sufficient conditions for the existence of traveling wave solutions are derived by the partial quasi-monotone condition,the Schauder's fixed-point theorem,and the upper-lower solutions method.Finally,the non-existence of traveling wave solutions for a nonlocal dispersal SEIR epidemic model is proved by the comparison principle.