摘要
建立和研究具接种疫苗年龄结构的MSIS流行病模型;总人口数服从N’(t)=f(N)N-μN;运用微分方程理论、积分方程理论得到一个与接种疫苗有关的再生数R(ψ)的表达式;证明当β<μ+γ时,无病平衡态是全局吸引的;当R(ψ)<1时,无病平衡态是局部渐近稳定的,当R(ψ)>1时,无病平衡态是不稳定的,此时存在一个局部渐近稳定的地方病平衡态。
In this paper, a variable periods MSIS epidemic model with the loss of immunity and an age-dependent vaccination rate ψis discussed; the overall population accords to the formula N＇ （t）= f（N）N-μN. By using the theory of differential or integral equation, an explicit formula for the vaccine -dependent reproductive number R （ψ is obtained. If R （ψis larger than one and condition β〈μ＋γ is held, then the disease-free equilibrium is global attractor. There exists an endemic steady state in this model under the condition of R （ψ 〈 1. Moreover, the endemic steady is locally asymptotically stable, if condition R（ψ 〉 1 is held.
出处
《江苏技术师范学院学报》
2005年第6期30-35,共6页
Journal of Jiangsu Teachers University of Technology
