| Volume 7, Number 1, 2017, Pages 147-171 DOI：10.11948/2017011 |
| Traveling Waves of a Reaction-Diffusion SIRQ Epidemic Model with Relapse |
| Chengcheng Zhu,Wantong Li,Feiying Yang |
| Keywords:Reaction-diffusion equations, basic reproduction number, traveling wave solutions, Schauder's fixed-point theorem, Lyapunov functional. |
| Abstract: |
| This paper is concerned with the traveling waves of a reaction-diffusion SIRQ epidemic model with relapse. We find that the existence and nonexistence of traveling waves are determined by the basic reproduction number of the system and the minimal wave speed. This threshold dynamics is proved by Schauder's fixed-point theorem combining Lyapunov functional with the theory of asymptotic spreading. Moreover, the numerical simulations are provided to illustrate our analytical results and the effect of the relapse is also discussed. |
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