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Traveling Waves of a Reaction-Diffusion SIRQ Epidemic Model with Relapse |
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| Authors: | Chengcheng Zhu Wantong Li Feiying Yang |
| Affiliation: | School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China,School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China and School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China |
| 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. |
| Keywords: | Reaction-diffusion equations basic reproduction number traveling wave solutions Schauder''s fixed-point theorem Lyapunov functional. |
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