摘要
考虑了具有周期传染率的SIR流行病模型.定义了基本再生数■_0=■/(μ+γ),分析了该模型的动力学性态,证明了■_0<1时无病平衡点是全局稳定的;■_0>1时,无病平衡点是不稳定的,模型至少存在一个周期解.对小振幅的周期传染率模型,给出了模型周期解的近似表达式,证明了该周期解的稳定性,最后做了数值模拟,结果显示周期解可能是全局稳定的.
In this paper a SIR model with periodic infection rate β(t) is studied. The basic reproductive number ^-R0= β/(μ+γ) is defined. The dynamical behavior of the model is analyzed. It is proved that the disease free equilibrium is globally stable if ^-R0〈 1. The disease free equilibrium is unstable when ^-R0〉 1. The existence of the periodic solution is investigated, and it is proved that the periodic model has at least one periodic solution if ^-R0〉 1. The unique- ness and stability of the periodic solution for sufficient small periodicity is obtained. We have the conjecture that the periodic endemic sohltion is globally stable when ^-R0〉 1. The numerical simulation suooorts our conjecture.
出处
《生物数学学报》
CSCD
北大核心
2008年第1期91-100,共10页
Journal of Biomathematics
基金
"十五"国家医学科技攻关课题资助项目.(编号:2004BA719A01)
关键词
周期传染率
重合度
周期解
Periodic infection rate
Coincidence degree
Periodic solution