具有Logistic输入和密度制约的一类阶段结构传染病模型

A Class of Stage-structured Epidemic Model with Logistic Input and Density Dependence

研究了一类将种群分为幼年和成年,假设成年个体患病,幼年个体受密度制约的具有Logistic输入的阶段结构传染病模型,得到了阶段结构种群的基本再生数和传染病的基本再生数。利用Hurwitz判据和构造Lyapunov函数,运用LaSalle不变性原理的方法,证明了R0和Re0满足一定条件时平衡点的局部稳定性和全局稳定性。最后,利用Matlab进行了数值模拟,验证了所得结果的正确性。

In this paper,we studied a class of stage-structured infectious disease models with logistic input and density dependence,and obtained the basic reproduction number of stage structured model and the infectious disease.The population was divided into youth and adult,and assume only adult individuals can be infected,young individuals are restricted by density.By using Hurwitz criterion and construct Lyapunov function,and by using LaSalle invariant principle,the local and global stability of equilibrium point is proved when R0 and Re0 satisfy certain conditions.Finally,numerical simulation is carried out by Matlab to verify the results.