摘要
研究具有连续预防接种和脉冲预防接种的SIR乙肝传染病模型,获得了再生数σ0和σ1.在连续模型中,当σ0<1时仅有无病平衡点存在,全局渐近稳定;σ0>1时无病平衡点不稳定,地方病平衡点存在,全局渐近稳定.在脉冲模型中,当σ1<1时无病周期解存在稳定;σ1>1时无病周期解不稳定,且在接种率充分小时,地方病周期解存在稳定.
Vaccination is an important strategy for the elimination of infectious diseases. Two mathematical SIR models with proportional vaccination and pulse vaccination are formulated in this paper. The dynamical behavior of these models are studied, and the basic reproductive numbers σ0 and σ1 are defined. For proportional model it is proved that the disease free equilibrium is globally asymptotically stable if σ0< 1, and it is unstable if σ0 >;the endemic equilibrium is globally asymptotically stable if σ0 > 1. For pulse model,it is proved that the disease free periodic solution is stable if σ1 < 1, and it is unstable if σ1 >; the endemic periodic solution is stable if σ1>1 and p is sufficiently small.
出处
《生物数学学报》
CSCD
2004年第2期149-155,共7页
Journal of Biomathematics
关键词
传染病模型
预防接种
再生数
平衡点
周期解
稳定性
epidemic model 5 Vaccination
Basic reproductive number
Equilibrium point
Periodic solution
Stability
