本文選題：傳染病模型　切入點(diǎn)：有限醫(yī)療資源　出處：《東北師范大學(xué)》2012年博士論文

【摘要】：本文的主要目的是研究有限醫(yī)療資源對(duì)傳染病傳播動(dòng)力學(xué)的影響,以及分析在有限醫(yī)療資源條件下的控制策略問題. 第一章為緒論.介紹傳染病動(dòng)力學(xué)、本文的主要工作和預(yù)備知識(shí). 第二章研究了有限治療資源及其供應(yīng)效率對(duì)SIR傳染病模型動(dòng)力學(xué)的影響.以有限治療資源的量及其供應(yīng)效率為參數(shù)確定了后向分支發(fā)生的充要條件,及后向分支發(fā)生時(shí)可用于疾病控制的有效閾值；并給出了Hopf分支的存在性、分支方向及穩(wěn)定性結(jié)果. 第三章利用多群體SIR傳染病模型,研究了疫苗資源的有限性和不同群體的特性對(duì)傳染病的傳播和控制的影響.確定了將有限疫苗資源僅用在部分子群體中,而實(shí)現(xiàn)消除整個(gè)群體中的傳染病的條件；同時(shí),定量研究了“優(yōu)先混合”接觸等群體特性對(duì)利用有限疫苗資源控制傳染病的影響,得到了提高群體自身內(nèi)部接觸比例會(huì)減小疫苗接種策略有效性的結(jié)論. 第四章通過建立包括羊和人在內(nèi)的傳染病動(dòng)力學(xué)模型,分析了我國(guó)內(nèi)蒙古地區(qū)布魯氏菌人畜共患病的流行趨勢(shì)、關(guān)鍵傳播因素和有限資源條件下的最優(yōu)控制策略.結(jié)果表明,現(xiàn)有控制措施并不能有效控制布病在內(nèi)蒙古地區(qū)的傳播,加強(qiáng)布病羊的撲殺和適當(dāng)控制羊群養(yǎng)殖規(guī)模是除羊群疫苗接種和預(yù)防措施宣傳教育之外,控制布病流行的另外兩個(gè)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.
【學(xué)位授予單位】：東北師范大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2012
【分類號(hào)】：R311;O175

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