Wave propagation in a diffusive SEIR epidemic model with nonlocal transmission and a general nonlinear incidence rate
Abstract We introduce a diffusive SEIR model with nonlocal delayed transmission between the infected subpopulation and the susceptible subpopulation with a general nonlinear incidence. We show that our results on existence and nonexistence of traveling wave solutions are determined by the basic repr...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-10-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-021-01564-z |
| _version_ | 1818690351208071168 |
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| author | Xin Wu Zhaohai Ma |
| author_facet | Xin Wu Zhaohai Ma |
| author_sort | Xin Wu |
| collection | DOAJ |
| description | Abstract We introduce a diffusive SEIR model with nonlocal delayed transmission between the infected subpopulation and the susceptible subpopulation with a general nonlinear incidence. We show that our results on existence and nonexistence of traveling wave solutions are determined by the basic reproduction number R 0 = ∂ I F ( S 0 , 0 ) / γ $R_{0}=\partial _{I}F(S_{0},0)/\gamma $ of the corresponding ordinary differential equations and the minimal wave speed c ∗ $c^{*}$ . The main difficulties lie in the fact that the semiflow generated here does not admit the order-preserving property. In the present paper, we overcome these difficulties to obtain the threshold dynamics. In view of the numerical simulations, we also obtain that the minimal wave speed is explicitly determined by the time delay and nonlocality in disease transmission and by the spatial movement pattern of the exposed and infected individuals. |
| first_indexed | 2024-12-17T12:24:37Z |
| format | Article |
| id | doaj.art-0a9a8a4a39994bb5806662e7ca3a9c67 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-17T12:24:37Z |
| publishDate | 2021-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-0a9a8a4a39994bb5806662e7ca3a9c672022-12-21T21:48:48ZengSpringerOpenBoundary Value Problems1687-27702021-10-012021113210.1186/s13661-021-01564-zWave propagation in a diffusive SEIR epidemic model with nonlocal transmission and a general nonlinear incidence rateXin Wu0Zhaohai Ma1School of Sciences, East China JiaoTong UniversitySchool of Science, China University of GeosciencesAbstract We introduce a diffusive SEIR model with nonlocal delayed transmission between the infected subpopulation and the susceptible subpopulation with a general nonlinear incidence. We show that our results on existence and nonexistence of traveling wave solutions are determined by the basic reproduction number R 0 = ∂ I F ( S 0 , 0 ) / γ $R_{0}=\partial _{I}F(S_{0},0)/\gamma $ of the corresponding ordinary differential equations and the minimal wave speed c ∗ $c^{*}$ . The main difficulties lie in the fact that the semiflow generated here does not admit the order-preserving property. In the present paper, we overcome these difficulties to obtain the threshold dynamics. In view of the numerical simulations, we also obtain that the minimal wave speed is explicitly determined by the time delay and nonlocality in disease transmission and by the spatial movement pattern of the exposed and infected individuals.https://doi.org/10.1186/s13661-021-01564-zTraveling wavesSEIR modelNonlinear incidenceSchauder fixed point theoremLaplace transform |
| spellingShingle | Xin Wu Zhaohai Ma Wave propagation in a diffusive SEIR epidemic model with nonlocal transmission and a general nonlinear incidence rate Boundary Value Problems Traveling waves SEIR model Nonlinear incidence Schauder fixed point theorem Laplace transform |
| title | Wave propagation in a diffusive SEIR epidemic model with nonlocal transmission and a general nonlinear incidence rate |
| title_full | Wave propagation in a diffusive SEIR epidemic model with nonlocal transmission and a general nonlinear incidence rate |
| title_fullStr | Wave propagation in a diffusive SEIR epidemic model with nonlocal transmission and a general nonlinear incidence rate |
| title_full_unstemmed | Wave propagation in a diffusive SEIR epidemic model with nonlocal transmission and a general nonlinear incidence rate |
| title_short | Wave propagation in a diffusive SEIR epidemic model with nonlocal transmission and a general nonlinear incidence rate |
| title_sort | wave propagation in a diffusive seir epidemic model with nonlocal transmission and a general nonlinear incidence rate |
| topic | Traveling waves SEIR model Nonlinear incidence Schauder fixed point theorem Laplace transform |
| url | https://doi.org/10.1186/s13661-021-01564-z |
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