具有限医疗资源传染病动力学模型分析

发布时间：2018-04-06 01:27

本文选题：传染病模型　切入点：有限医疗资源　出处：《东北师范大学》2012年博士论文

【摘要】：本文的主要目的是研究有限医疗资源对传染病传播动力学的影响,以及分析在有限医疗资源条件下的控制策略问题. 第一章为绪论.介绍传染病动力学、本文的主要工作和预备知识. 第二章研究了有限治疗资源及其供应效率对SIR传染病模型动力学的影响.以有限治疗资源的量及其供应效率为参数确定了后向分支发生的充要条件,及后向分支发生时可用于疾病控制的有效阈值；并给出了Hopf分支的存在性、分支方向及稳定性结果. 第三章利用多群体SIR传染病模型,研究了疫苗资源的有限性和不同群体的特性对传染病的传播和控制的影响.确定了将有限疫苗资源仅用在部分子群体中,而实现消除整个群体中的传染病的条件；同时,定量研究了“优先混合”接触等群体特性对利用有限疫苗资源控制传染病的影响,得到了提高群体自身内部接触比例会减小疫苗接种策略有效性的结论. 第四章通过建立包括羊和人在内的传染病动力学模型,分析了我国内蒙古地区布鲁氏菌人畜共患病的流行趋势、关键传播因素和有限资源条件下的最优控制策略.结果表明,现有控制措施并不能有效控制布病在内蒙古地区的传播,加强布病羊的扑杀和适当控制羊群养殖规模是除羊群疫苗接种和预防措施宣传教育之外,控制布病流行的另外两个重要因素.
[Abstract]:The main purpose of this paper is to study the influence of limited medical resources on the dynamics of infectious disease transmission and to analyze the control strategy under the condition of limited medical resources.The first chapter is the introduction.This paper introduces the dynamics of infectious diseases, the main work and preparatory knowledge of this paper.In chapter 2, the effects of limited treatment resources and their supply efficiency on the dynamics of SIR infectious disease model were studied.The sufficient and necessary conditions for the occurrence of backward branches and the effective threshold for disease control at the time of occurrence of backward branches are determined by taking the quantity of limited therapeutic resources and their supply efficiency as parameters, and the existence, direction and stability of Hopf branches are given.In chapter 3, the effects of the limitation of vaccine resources and the characteristics of different populations on the transmission and control of infectious diseases are studied by using the multi-population SIR model.Determining the conditions under which limited vaccine resources can be used only in partial subpopulations to achieve the elimination of infectious diseases in the whole population, and at the same time, quantitatively studying the effects of population characteristics such as "priority mix" exposure on the use of limited vaccine resources for the control of infectious diseases,It is concluded that increasing the proportion of internal exposure will reduce the effectiveness of vaccination strategy.In chapter 4, the epidemic trend of brucella zoonosis in Inner Mongolia, the key transmission factors and the optimal control strategy under limited resources are analyzed by establishing a dynamic model of infectious diseases, including sheep and human beings.The results showed that the existing control measures could not effectively control the spread of brucellosis in Inner Mongolia, and strengthening the culling of the sheep and controlling the scale of sheep breeding were not only the vaccination of sheep, but also the propaganda and education of prevention measures.Two other important factors in controlling the prevalence of brucellosis.
【学位授予单位】：东北师范大学
【学位级别】：博士
【学位授予年份】：2012
【分类号】：R311;O175

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