Global dynamics of an epidemic model with relapse and nonlinear incidence. (13th December 2018)

• Record Type: Journal Article
• Authors: Chen, Yuming; Li, Jianquan; Zou, Shaofen
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 4(2019)
• Page Start: 1283
• Page End: 1291
• Publication Date: 2018-12-13
• Subjects: fluctuation lemma -- global stability -- immunity -- Lyapunov function -- nonlinear incidence -- relapse; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5439
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : On the basis of a basic SIR epidemic model, we propose and study an epidemic model with nonlinear incidence. The model also incorporates many features of the recovered such as relapse and with/without immunity. A threshold dynamics is established, which is completely determined by the basic reproduction number. The global stability of the disease‐free equilibrium is proved by means of the fluctuation lemma. To prove the global stability of the endemic equilibrium, we need some novel techniques including the transformation of variables, the construction of a new type of Lyapunov functions, and the seeking of an appropriate positively invariant set of the model.