Propagation Dynamics of an Age‐Structured SI Infectious Disease Model With Spatial Diffusion

ABSTRACT This paper is concerned with traveling wave solutions and spreading speeds of an age‐structured infectious disease model with spatial diffusion and a general incidence function. We first establish criteria for the existence and nonexistence of traveling wave solutions, and determine the minimal wave speed. Then, we employ uniform persistence theory to derive the asymptotic spreading speeds of the infection. Our results reveal that, owing to the finite maximum age of the population, individuals in all age groups exhibit an asymptotically uniform spreading speed. To the best of our knowledge, this is the first work to analyze spreading speeds of a nonmonotonic age‐structured epidemic model.