Global dynamics of an SVEIR epidemic model with distributed delay and nonlinear incidence

被引:30
作者
Wang, Lianwen [1 ]
Liu, Zhijun [2 ]
Zhang, Xingan [1 ]
机构
[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
[2] Hubei Univ Nationalities, Dept Math, Enshi 445000, Hubei, Peoples R China
基金
中国国家自然科学基金;
关键词
SVEIR model; Vaccination; Nonlinear incidence; Infinite distributed delay; Global stability; Lyapunov functional; INFECTIOUS-DISEASES; VARYING INFECTIVITY; MEDIA COVERAGE; THRESHOLD DYNAMICS; INFINITE DELAY; MUMPS VACCINE; STABILITY; IMPACT; TRANSMISSION; RELAPSE;
D O I
10.1016/j.amc.2016.02.058
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
An SVEIR epidemic model with imperfect vaccination and nonlinear incidence, and a general latent distribution is formulated. By constructing Lyapunov functionals, it is shown that the disease will die out if the vaccination reproduction number R-vac <= 1 and the disease becomes endemic if R-vac > 1. Furthermore, vaccination effects are analyzed. Two special forms the probability of remaining in latent class are discussed. When the probability is negatively exponentially distributed, we present an efficient approach of proving global stability of the endemic equilibrium of the SVEIR system of ordinary differential equations (ODEs), which may improve some known approaches. When the probability is a step-function, the delay differential equation (DDE) system derived is used to study the impacts of vaccination and saturated incidence on the mumps transmission. (C) 2016 Elsevier Inc. All rights reserved.
引用
收藏
页码:47 / 65
页数:19
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