期刊
DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS
卷 30, 期 1, 页码 1-22出版社
SPRINGER INDIA
DOI: 10.1007/s12591-018-0408-8
关键词
SIS epidemic model; Vaccine-age; Asymptotic smoothness; Uniform persistence; Global stability
资金
- National Natural Science Foundation of China [11371368]
- Natural Science Foundation of Hebei Province [A2014506015, A2016506002]
- Science Foundation of Shijiazhuang Mechanical Engineering College [YJJXM 13008, JCYJ14011]
This paper investigates an SIS epidemic model with age of vaccination. It proves the asymptotic smoothness of the semi-flow and discusses the local stability of a disease-free steady state and an endemic steady state by analyzing the corresponding characteristic equations. It shows that the system is permanent if the basic reproduction number is greater than unity. By constructing two Lyapunov functionals, it proves that the endemic steady state is globally asymptotically stable when the basic reproduction number is greater than unity, and derives sufficient conditions for the global asymptotic stability of the disease-free steady state. Numerical simulations are provided to illustrate the asymptotic stabilities of the disease-free steady state and endemic state.
In this paper, an SIS epidemic model with age of vaccination is investigated. Asymptotic smoothness of the semi-flow is proved. By analyzing the corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state is discussed. It is shown that if the basic reproduction number is greater than unity, the system is permanent. By constructing two Lyapunov functionals, it is proved that the endemic steady state is globally asymptotically stable if the basic reproduction number is greater than unity, and sufficient conditions are derived for the global asymptotic stability of the disease-free steady state. Numerical simulations are given to illustrate the asymptotic stabilities of the disease-free steady state and endemic state.
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