Wave propagation of a diffusive epidemic model with latency and vaccination

Abstract

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.

Keywords:

• Diffusive epidemic model
• traveling wave solutions
• latent period
• vaccination strategy

2010 Mathematics Subject Classifications:

• 34D23
• 35C07
• 35Q92

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by National Natural Science Foundation of China [grant number 11571326 and 11901543].