The strong waves for a non-local dispersal epidemic model with latent stage and multiple parallel infectious stages

Considering the phenomenon of multiple parallel infection and latent stages in the spatial spread of the disease, a non-local dispersal epidemic model, which describes such a mechanism of disease transmission, is proposed. Our attention is directed toward the existence of strong traveling wave solutions connecting disease-free equilibrium and endemic equilibrium using the fixed point theorem, the method of upper–lower solutions and some limit techniques. When the basic reproduction number [Formula: see text], a unique critical wave speed [Formula: see text] is defined, and then when wave speed [Formula: see text], the existence of the traveling wave solution is established. In particular, the existence of strong wave solutions at wave speed [Formula: see text] is also discussed. Furthermore, when [Formula: see text] and [Formula: see text] or [Formula: see text] and [Formula: see text], the non-existence of traveling wave solution also is established. Finally, we present the numerical simulations and investigate the effect of the critical wave speed and non-local diffusion on disease propagation.