SPATIAL DYNAMICS OF A NONLOCAL DISPERSAL VECTOR DISEASE MODEL WITH SPATIO-TEMPORAL DELAY

This article concerns the spatial dynamics of a nonlocal dispersal vector disease model with spatio-temporal delay. We establish the existence of spreading speeds and construct some new types of solutions which are different from the traveling wave solutions. To obtain the existence of spreading speed, we follow the truncating approach to develop a comparison principle and to construct a suitable sub-solution. Our result indicates that the spreading speed coincides with the minimal wave speed of the regular traveling waves. The solutions are constructed by combining regular traveling waves and the spatially independent solutions which provide some new transmission forms of the disease.