Existence of traveling wave solutions for an infection-age structured model with population diffusion

This paper studies an epidemic model that incorporates the population diffusion and infection age. The threshold conditions for the existence of traveling wave solutions are established, which answer two open problems in Ducrot and Magal (Nonlinearity, 24 (2011), 2891-2911). More specifically, the restriction for the diffusion coefficients of susceptible population and infectious population is removed and the existence of traveling wave solution with critical wave speed is obtained.