年龄结构流行病模型基本再生数数值计算  

Numerical Approximation of Basic Reproduction Number for an Age-structure Epidemic System

作　　者：卢琴[1] 郭文娟 LU Qin;GUO Wen-juan(China University Of Mining And Technology Yinchuan College,Yinchuan 750021,China;School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,China)

机构地区：[1]中国矿业大学银川学院,宁夏银川750021 [2]宁夏大学数学统计学院,宁夏银川750021

出　　处：《数学的实践与认识》2021年第11期146-153,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11661064);中国矿业大学银川学院校级项目(XJJG2019002)。

摘　　要：通常情况下,年龄结构的流行病模型基本再生数R0很难给出显式表达式,利用了θ方法,对感染个体产生的线性算子在有限水平上离散,将抽象问题转化为求解下一代矩阵的正主特征值的问题,根据谱逼近理论,得到当n→+∞,R0,n→R0.数值结果验证了理论结果.Generally speaking,R0 cannot be explicitly calculated for most age-structured epidemic systems.In this paper,we discretize a linear operator produced by the infective population with a theta scheme in a finite horizon,which transforms the abstract problem into the problem of solving the positive dominant eigenvalue of the next-generation matrix.This leads to a corresponding threshold R0,n.Using the spectral approximation theory,we obtain that R0,n→R0 as n→+∞.Some numerical simulations are provided to certify the theoretical results.

关 键 词：基本再生数 θ算法 流行病模型 

分 类 号：O175[理学—数学] R181.1[理学—基础数学]