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Global stability of a multi‐group model with distributed delay and vaccination
Author(s) -
Xu Jinhu,
Geng Yan,
Zhou Yicang
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4068
Subject(s) - mathematics , mathematical proof , stability theory , lyapunov function , epidemic model , basic reproduction number , stability (learning theory) , graph , exploit , group (periodic table) , discrete mathematics , computer science , demography , nonlinear system , population , chemistry , physics , geometry , computer security , organic chemistry , quantum mechanics , machine learning , sociology
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 numberℜ 0 vacplays a key role in the dynamics of the model: the disease‐free equilibrium is globally asymptotically stable whenℜ 0 vac ≤ 1 , while the endemic equilibrium exists uniquely and is globally asymptotically stable whenℜ 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.