Threshold Dynamics of an SIR Model with Nonlinear Incidence Rate and Age-Dependent Susceptibility. (14th October 2018)

• Record Type: Journal Article
• Authors: Yang, Junyuan; Wang, Xiaoyan
• Other Names: Amancio Diego R. Academic Editor.
• Is Part Of: Complexity. Volume 2018(2018)
• Publication Date: 2018-10-14
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2018/9613807
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : 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 ℛ 0 and some assumptions for the incidence rate.