Global stability of an SEIR epidemic model with age-dependent latency and relapse. (August 2015)

• Record Type: Journal Article
• Authors: Liu, Lili; Wang, Jinliang; Liu, Xianning
• Is Part Of: Nonlinear analysis. Volume 24(2015)
• Page Start: 18
• Page End: 35
• Publication Date: 2015-08
• Subjects: SEIR epidemic model -- Age-dependent latency -- Age-dependent relapse -- Global stability -- Lyapunov functional; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2015.01.001
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, an SEIR epidemic model for a disease with age-dependent latency and relapse is proposed. Such a model is very appropriate for tuberculosis and herpes. The basic reproduction number ℜ 0 is defined and proved as a classic threshold parameter. Asymptotic smoothness of solutions and uniform persistence of the system are shown via reformulating the system as a system of Volterra integral equations. The local stability and global stability of equilibria are obtained by analyzing the corresponding characteristic equations and constructing the proper Volterra-type Lyapunov functionals, respectively. Finally, some special cases of the model as key functions reducing to constant are discussed in the last section.