几类传染病模型中基本再生数的计算

摘要

This paper introduces the derivation of basic reproduction numbers for several epidemic models.The basic reproduction number plays an important role in describing the dynamic behavior of infectious disease models,which is an important indicator to determine the prevalence of diseases.Therefore,the basic reproductive number is a significant reference for the prevention and control of diseases and the immunization strategy.The basic reproduction numbers can be derived by means of the definition,the monotonicity of the infected individuals at the initial moment,the existence of the positive equilibrium and the local stability of the disease-free equilibrium,the numerical simulation,respectively.This paper introduces many epidemic models especially network model and calculates their basic reproduction numbers.Finally,we analyze the changes in the basic reproduction numbers during different periods.%通过参考大量文献,系统整理了几类经典的传染病模型,并对传染病模型基本再生数的几种导出方法做了一个综述.文中综合了传染病动力学模型的分析方法和复杂网络理论,分别从基本再生数的定义,初始时刻染病者的单调性,正平衡点的存在性,无病平衡点的局部稳定性,即通过计算基本再生矩阵或者雅克比矩阵的特征值,数值模拟,这几个角度给出了基本再生数的导出方法,并举例说明了几类主要的传染病模型,特别是网络传播模型中基本再生数的计算方法,给出了基本再生数的特点,并对基本再生数时变的情况进行了具体分析.