Wave propagation of a diffusive epidemic model with latency and vaccination

In this paper, we consider a diffusive epidemic model with latent period and vaccination strategy. The well-posedness of solutions is first investigated for such a system. Then, in terms of the basic reproduction number and the critical wave speed, we establish a complete threshold result which reveals the existence and nonexistence of the strong traveling waves connecting the disease-free equilibrium to the endemic steady state. Finally, some numerical simulations are performed to illustrate our theoretical analysis. Our results implies that (i) the diffusion ability of the infected individuals can accelerate the minimal wave speed; and (ii) the latent period and vaccination strategy would slow down the spread of the disease.

Automated summary

This paper investigates a diffusive epidemic model with latent period and vaccination strategy, establishing a threshold result based on the basic reproduction number and critical wave speed. The results imply that the diffusion ability of infected individuals can accelerate the minimal wave speed, while the latent period and vaccination strategy can slow down the spread of the disease.