具有年龄结构的手足口病模型的动力学分析

Threshold dynamics of an age-structured HFMD model

根据手足口病的传播与宿主年龄结构有关的特点,建立并分析了一类具有年龄结构的手足口病传播模型。利用半群方法得到了模型的正性,给出了模型的基本再生数R_(0),利用线性化方法和Fatou引理证明了当R_(0)<1时无病平衡点是全局渐近稳定的,即疾病绝灭。证明了当R_(0)>1时,模型存在唯一的地方病平衡态,并给出了模型局部稳定的充分条件,即R 0>1时疾病存在。

Given the transmission of hand-foot-mouth disease(HFMD)is related to the age structure of the host,an age-structured model for the disease transmission dynamics of HFMD is formulated and analyzed.The positivity of the model is obtained by using the semigroup method,and then the basic reproduction number of the model is given,by the linearization method and Fatou lemma.It is proved that the disease-free equilibrium is globally asymptotically stable if R_(0)<1,the disease dies out.It is proved that there is a unique disease-endemic steady state if R_(0)>1.The local stability conditions for the disease-endemic steady state is also given,and the disease exists.