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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Main Authors: Junyuan Yang, Xiaoyan Wang
Format: Article
Language:English
Published: Wiley 2018-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2018/9613807
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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.
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language English
publishDate 2018-01-01
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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