【摘要】 研究了一类具有垂直传染的年龄结构SIS传染病模型。在总人口规模不变的假设下,得到了疾病消亡与否的基本再生数T的表达式。证明了当T<1时,无病平衡解局部渐近稳定,此时疾病消亡;当T>1时,无病平衡解不稳定,此时系统存在唯一地方病平衡解,并在一定条件下证明了地方病平衡解的局部渐近稳定。更多还原

【Abstract】 An age-structured SIS epidemic model with vertical transmission is discussed.With the assumption that the total population is invariant in the model,the basic reproduction number T which determines the extinction of epidemic disease is obtained.The disease-free equilibrium is locally asymptotically stable when the basic reproduction number T <1,that is to say the disease is extinct.The disease-free equilibrium is unstable when the basic reproduction number T >1,and a positive endemic solution appears which is also locally asymptotically stable under a certain condition.更多还原