一类具有一般出生函数阶段结构的传染病模型的全局分析

Global Analysis for an Epidemic Model with the General Birth Function and Stage Structure

假设种群个体生长分幼年和成年两个阶段以及疾病仅在成年阶段传播,建立并研究了一类幼年个体输入率为一般函数的传染病模型,得到了决定种群存活与否的种群存活基本再生数和决定疾病传播灭绝与否的疾病传播基本再生数,通过构造适当的Lyapunov函数分析了模型的全局阈值动力学性态.

In this paper,under the assumption that the individual growth of the population consists of two stages:juvenile and adult,and that the infection is transmitted only between the adults,an epidemic model with a general form of birth function of the juveniles is established and investigated.The basic reproduction number of the population survival determining if the population persists and the basic reproduction number of the infection transmission determining if the disease dies out are found.The global threshold dynamics of the model is obtained by constructing the appropriate Lyapunov functions.