Abstract | With the assumptions that an infectious disease in a poulation has a fixed latent period and the latent individuals of the population may diffuse, we formulate an SIR model with a simple demographical structure for the population living in a spatially continuous environment. The model is given by a system of reaction-diffusion equations with a discrete delay accounting for the latency and a spatially non-local term caused by the mobility of the individuals during the latent period. We address the existence, uniqueness and positivity of solution to the initial-value problem for this type of system. Moreover, we investigate the traveling wave fronts of the system and obtain a critical value c* which is a lower bound for the wave speed of the traveling wave fronts. Furthermore, the simulations on the PDE model also suggest that the spread speed of the disease indeed coincides with c*. We also discuss how the model parameters affect c*. |