The Propagation Phenomena In A Nonlocal Epidemic Model With Standard Incidence

Nonlocal operators describe distance diffusion much better than classical Laplace operators,more and more nonlocal diffusive equations is used to model the diffusion of epidemics.Since traveling waves can represent the transmission of the epidemics well,the traveling wave solutions of nonlocal diffusive epidemic model get much more attention.In present paper,we first consider a nonlocal diffusive SEIR epidemic model with standard incidence where the spread of infections is local.Since the regularity and compactness of the nonlocal diffusive operators are deficient,there is much trouble in our work.We use the truncation method to deal with it.The existence of traveling waves is proved by constructing a closed cone in a large bounded domain,and applying Schauder's fixed-point theorem on this cone,then passing to the unbounded domain,when the basic reproduction number R₀> 1.Nonexistence is testified by two Laplace transform,when the basic reproduction number R₀? 1 or R₀> 1 and c < c^*,where c^* is the minimal speed of traveling waves.After that,a nonlocal reaction-diffusion SEIR model with standard incidence is investigated.Through an eigenvector method and Schauder's fixed-piont theorem,we obtain the existence of traveling waves too.What's different is that we use a unusual method to obtain the exponent estimates,which is necessary to use Laplace transform.