Travelling waves in an infectious disease model with a fixed latent period and a spatio-temporal delay

This paper is concerned with the existence of travelling waves to an infectious disease model with a fixed latent period and a spatio-temporal delay. By analyzing the corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state to this model is discussed. By constructing a pair of upper-lower solutions, we use the cross iteration method and the Schauder's fixed point theorem to prove the existence of a travelling wave solution connecting the disease-free steady state and the endemic steady state. Numerical simulations are carried out to illustrate the main results.