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 |
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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 |
| _version_ | 1797830578519670784 |
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| author | Wu Pei Qiaoshun Yang Zhiting Xu |
| author_facet | Wu Pei Qiaoshun Yang Zhiting Xu |
| author_sort | Wu Pei |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-09T13:38:19Z |
| format | Article |
| id | doaj.art-5ee7669f9b2647479480a148cc8c0ccb |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:38:19Z |
| publishDate | 2017-11-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-5ee7669f9b2647479480a148cc8c0ccb2023-05-09T07:53:07ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752017-11-0120178211910.14232/ejqtde.2017.1.825732Traveling waves of a delayed epidemic model with spatial diffusionWu Pei0Qiaoshun Yang1Zhiting Xu2Department of Mathematics and Computer Science, Normal College, Jishou University, Jishou Hunan, P.R. ChinaDepartment of Mathematics and Computer Science, Normal College, Jishou University, Jishou, Hunan, P.R. ChinaSouth China Normal University, Guangzhou, P.R. ChinaIn 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.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5732traveling wave solutionsdelayed epidemic modelschauder fixed point theoremlyapunov functional |
| spellingShingle | Wu Pei Qiaoshun Yang Zhiting Xu Traveling waves of a delayed epidemic model with spatial diffusion Electronic Journal of Qualitative Theory of Differential Equations traveling wave solutions delayed epidemic model schauder fixed point theorem lyapunov functional |
| title | Traveling waves of a delayed epidemic model with spatial diffusion |
| title_full | Traveling waves of a delayed epidemic model with spatial diffusion |
| title_fullStr | Traveling waves of a delayed epidemic model with spatial diffusion |
| title_full_unstemmed | Traveling waves of a delayed epidemic model with spatial diffusion |
| title_short | Traveling waves of a delayed epidemic model with spatial diffusion |
| title_sort | traveling waves of a delayed epidemic model with spatial diffusion |
| topic | traveling wave solutions delayed epidemic model schauder fixed point theorem lyapunov functional |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5732 |
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