Global stability of a multi‐group model with distributed delay and vaccination. (1st July 2016)

• Record Type: Journal Article
• Authors: Xu, Jinhu; Geng, Yan; Zhou, Yicang
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 5(2017)
• Page Start: 1475
• Page End: 1486
• Publication Date: 2016-07-01
• Subjects: multi‐group model -- distributed delay -- vaccination -- Lyapunov functionals -- globally asymptotically stable; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4068
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : A delayed multi‐group SVEIR epidemic model with vaccination and a general incidence function has been formulated and studied in this paper. Mathematical analysis shows that the basic reproduction number ℜ 0 vac plays a key role in the dynamics of the model: the disease‐free equilibrium is globally asymptotically stable when ℜ 0 vac ≤ 1, while the endemic equilibrium exists uniquely and is globally asymptotically stable when ℜ 0 vac > 1 . For the proofs, we exploit a graph‐theoretical approach to the method of Lyapunov functionals. Our results show that distributed delay has no impact on the global stability of equilibria, and the results improve and generalize some known results. Copyright © 2016 John Wiley & Sons, Ltd.