Traveling waves of a delayed epidemic model with spatial diffusion
In this paper, we study the existence and non-existence of traveling waves for a delayed epidemic model with spatial diffusion. That is, by using Schauder's fixed-point theorem and the construction of Lyapunov functional, we prove that when the basic reproduction number $R_0>1$, there exists...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2017-11-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5732 |
| Summary: | In this paper, we study the existence and non-existence of traveling waves for a delayed epidemic model with spatial diffusion. That is, by using Schauder's fixed-point theorem and the construction of Lyapunov functional, we prove that when the basic reproduction number $R_0>1$, there exists a critical number $c^*>0$ such that for all $c>c^*$, the model admits a non-trivial and positive traveling wave solution with wave speed $c$. And for $c<c^*$, by the theory of asymptotic spreading, we further show that the model admits no non-trivial and non-negative traveling wave solution. And also, some numerical simulations are performed to illustrate our analytic results. |
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| ISSN: | 1417-3875 |