Traveling waves in nonlocal dispersal SIR epidemic model with nonlinear incidence and distributed latent delay
Abstract This paper studies the traveling waves in a nonlocal dispersal SIR epidemic model with nonlinear incidence and distributed latent delay. It is found that the traveling waves connecting the disease-free equilibrium with endemic equilibrium are determined by the basic reproduction number R 0...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-10-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-03073-2 |
| _version_ | 1818550580418707456 |
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| author | Weixin Wu Zhidong Teng |
| author_facet | Weixin Wu Zhidong Teng |
| author_sort | Weixin Wu |
| collection | DOAJ |
| description | Abstract This paper studies the traveling waves in a nonlocal dispersal SIR epidemic model with nonlinear incidence and distributed latent delay. It is found that the traveling waves connecting the disease-free equilibrium with endemic equilibrium are determined by the basic reproduction number R 0 $\mathcal{R}_{0}$ and the minimal wave speed c ∗ $c^{*}$ . When R 0 > 1 $\mathcal{R}_{0}>1$ and c > c ∗ $c>c^{*}$ , the existence of traveling waves is established by using the upper-lower solutions, auxiliary system, constructing the solution map, and then the fixed point theorem, limiting argument, diagonal extraction method, and Lyapunov functions. When R 0 > 1 $\mathcal{R}_{0}>1$ and 0 < c < c ∗ $0< c< c^{*}$ , the nonexistence result is also obtained by using the reduction to absurdity and the theory of asymptotic spreading. |
| first_indexed | 2024-12-12T08:48:21Z |
| format | Article |
| id | doaj.art-f420cdad9c164750b2e7705dbcb98476 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-12T08:48:21Z |
| publishDate | 2020-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-f420cdad9c164750b2e7705dbcb984762022-12-22T00:30:21ZengSpringerOpenAdvances in Difference Equations1687-18472020-10-012020112610.1186/s13662-020-03073-2Traveling waves in nonlocal dispersal SIR epidemic model with nonlinear incidence and distributed latent delayWeixin Wu0Zhidong Teng1College of Mathematics and Systems Science, Xinjiang UniversityCollege of Mathematics and Systems Science, Xinjiang UniversityAbstract This paper studies the traveling waves in a nonlocal dispersal SIR epidemic model with nonlinear incidence and distributed latent delay. It is found that the traveling waves connecting the disease-free equilibrium with endemic equilibrium are determined by the basic reproduction number R 0 $\mathcal{R}_{0}$ and the minimal wave speed c ∗ $c^{*}$ . When R 0 > 1 $\mathcal{R}_{0}>1$ and c > c ∗ $c>c^{*}$ , the existence of traveling waves is established by using the upper-lower solutions, auxiliary system, constructing the solution map, and then the fixed point theorem, limiting argument, diagonal extraction method, and Lyapunov functions. When R 0 > 1 $\mathcal{R}_{0}>1$ and 0 < c < c ∗ $0< c< c^{*}$ , the nonexistence result is also obtained by using the reduction to absurdity and the theory of asymptotic spreading.http://link.springer.com/article/10.1186/s13662-020-03073-2Nonlocal dispersal epidemic modelNonlinear incidenceDistributed latent delayTraveling wavesUpper-lower solutionsLimiting argument |
| spellingShingle | Weixin Wu Zhidong Teng Traveling waves in nonlocal dispersal SIR epidemic model with nonlinear incidence and distributed latent delay Advances in Difference Equations Nonlocal dispersal epidemic model Nonlinear incidence Distributed latent delay Traveling waves Upper-lower solutions Limiting argument |
| title | Traveling waves in nonlocal dispersal SIR epidemic model with nonlinear incidence and distributed latent delay |
| title_full | Traveling waves in nonlocal dispersal SIR epidemic model with nonlinear incidence and distributed latent delay |
| title_fullStr | Traveling waves in nonlocal dispersal SIR epidemic model with nonlinear incidence and distributed latent delay |
| title_full_unstemmed | Traveling waves in nonlocal dispersal SIR epidemic model with nonlinear incidence and distributed latent delay |
| title_short | Traveling waves in nonlocal dispersal SIR epidemic model with nonlinear incidence and distributed latent delay |
| title_sort | traveling waves in nonlocal dispersal sir epidemic model with nonlinear incidence and distributed latent delay |
| topic | Nonlocal dispersal epidemic model Nonlinear incidence Distributed latent delay Traveling waves Upper-lower solutions Limiting argument |
| url | http://link.springer.com/article/10.1186/s13662-020-03073-2 |
| work_keys_str_mv | AT weixinwu travelingwavesinnonlocaldispersalsirepidemicmodelwithnonlinearincidenceanddistributedlatentdelay AT zhidongteng travelingwavesinnonlocaldispersalsirepidemicmodelwithnonlinearincidenceanddistributedlatentdelay |