Propagation dynamics of a nonlocal dispersal Zika transmission model with general incidence

Abstract

In this paper, we are interested in propagation dynamics of a nonlocal dispersal Zika transmission model with general incidence. When the threshold is greater than one, we prove that there is a wave speed such that the model has a traveling wave solution with speed , and there is no traveling wave solution with speed less than . When the threshold is less than or equal to one, we show that there is no nontrivial traveling wave solution. The approaches we use here are Schauder's fixed point theorem with an explicit construction of a pair of upper and lower solutions, the contradictory approach, and the two‐sided Laplace transform.