Threshold Dynamics of an SIR Model with Nonlinear Incidence Rate and Age-Dependent Susceptibility
We propose an SIR epidemic model with different susceptibilities and nonlinear incidence rate. First, we obtain the existence and uniqueness of the system and the regularity of the solution semiflow based on some assumptions for the parameters. Then, we calculate the basic reproduction number, which...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/9613807 |
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| _version_ | 1850163066746961920 |
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| author | Junyuan Yang Xiaoyan Wang |
| author_facet | Junyuan Yang Xiaoyan Wang |
| author_sort | Junyuan Yang |
| collection | DOAJ |
| description | We propose an SIR epidemic model with different susceptibilities and nonlinear incidence rate. First, we obtain the existence and uniqueness of the system and the regularity of the solution semiflow based on some assumptions for the parameters. Then, we calculate the basic reproduction number, which is the spectral radius of the next-generation operator. Second, we investigate the existence and local stability of the steady states. Finally, we construct suitable Lyapunov functionals to strictly prove the global stability of the system, which are determined by the basic reproduction number ℛ0 and some assumptions for the incidence rate. |
| format | Article |
| id | doaj-art-ef2cb3cdee664de6b7ed6c3b0f1073ce |
| institution | OA Journals |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-ef2cb3cdee664de6b7ed6c3b0f1073ce2025-08-20T02:22:24ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/96138079613807Threshold Dynamics of an SIR Model with Nonlinear Incidence Rate and Age-Dependent SusceptibilityJunyuan Yang0Xiaoyan Wang1Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006, ChinaSchool of Information Management, Shanxi University of Finance and Economics, Taiyuan, Shanxi 030006, ChinaWe propose an SIR epidemic model with different susceptibilities and nonlinear incidence rate. First, we obtain the existence and uniqueness of the system and the regularity of the solution semiflow based on some assumptions for the parameters. Then, we calculate the basic reproduction number, which is the spectral radius of the next-generation operator. Second, we investigate the existence and local stability of the steady states. Finally, we construct suitable Lyapunov functionals to strictly prove the global stability of the system, which are determined by the basic reproduction number ℛ0 and some assumptions for the incidence rate.http://dx.doi.org/10.1155/2018/9613807 |
| spellingShingle | Junyuan Yang Xiaoyan Wang Threshold Dynamics of an SIR Model with Nonlinear Incidence Rate and Age-Dependent Susceptibility Complexity |
| title | Threshold Dynamics of an SIR Model with Nonlinear Incidence Rate and Age-Dependent Susceptibility |
| title_full | Threshold Dynamics of an SIR Model with Nonlinear Incidence Rate and Age-Dependent Susceptibility |
| title_fullStr | Threshold Dynamics of an SIR Model with Nonlinear Incidence Rate and Age-Dependent Susceptibility |
| title_full_unstemmed | Threshold Dynamics of an SIR Model with Nonlinear Incidence Rate and Age-Dependent Susceptibility |
| title_short | Threshold Dynamics of an SIR Model with Nonlinear Incidence Rate and Age-Dependent Susceptibility |
| title_sort | threshold dynamics of an sir model with nonlinear incidence rate and age dependent susceptibility |
| url | http://dx.doi.org/10.1155/2018/9613807 |
| work_keys_str_mv | AT junyuanyang thresholddynamicsofansirmodelwithnonlinearincidencerateandagedependentsusceptibility AT xiaoyanwang thresholddynamicsofansirmodelwithnonlinearincidencerateandagedependentsusceptibility |