经济效应下耐药肺结核的控制机理——基于传播模型的动力学分析  

The Control of Drug-Resistant Tuberculosis under Economic Effects——Based on the Dynamic Analysis of a Transmission Model

作　　者：张照旺 祝光湖[1] 唐甜[2] ZHANG Zhao-wang;ZHU Guang-hu;TANG Tian(School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China;School of Information and Communication,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004 [2]桂林电子科技大学信息与通信学院,广西桂林541004

出　　处：《数学的实践与认识》2023年第12期135-142,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11661026)。

摘　　要：首先根据肺结核的流行病特征、社会经济生成及其影响,结合耐药性,建立一个新的含经济效应的耐药肺结核传播新模型.接着利用微分方程定性理论、传染病动力学理论分析模型的动力学性质,包括求基本再生数、证明平衡点的稳定性等,并利用敏感性分析挖掘经济对肺结核疫情的影响效应,进一步讨论如何利用经济逃脱肺结核导致的经济陷阱.研究表明降低个体的感染率和加大对疫情高发地区及病人的经济补助能够有效控制疫情.结果可为肺结核疫情防控提供科学指导.A new transmission model for drug-resistant tuberculosis(TB)with economic effects is established based on TB epidemiology,socioeconomic generation and its impact.Using the theory of differential equations and infectious disease dynamics,the dynamics features of the model is clarified,in which the basic reproduction number is computed,and the stability of the equilibrium point is proved.It is further used sensitivity analysis to explore the impact of the economy on TB epidemic,and to clarify how to escape the economic-TB trap through financial assistance.The results show that reducing individual infection rate and increasing financial assistance for high-incidence regions and patients can effectively control TB epidemics.The results can provide scientific guidance for the prevention and control of TB infection.

关 键 词：经济效应 肺结核 稳定性 基本再生数 

分 类 号：O175[理学—数学] R521[理学—基础数学] R181[医药卫生—内科学]