【摘要】：本文主要依據(jù)傳染病模型免疫反應(yīng)中的“倉(cāng)室模型”,針對(duì)易感人群預(yù)防接種后仍會(huì)感染乙肝病毒這一現(xiàn)象,我們?cè)诖私⒘巳惥哂须A段結(jié)構(gòu)和免疫逃避的SIRS傳染病動(dòng)力學(xué)模型。進(jìn)而研究模型的動(dòng)力學(xué)性態(tài),并給出其生物學(xué)意義,全文主要分為以下五章。第一章,本章為全文的緒論。首先簡(jiǎn)單介紹了傳染病的發(fā)展簡(jiǎn)況和本文選題依據(jù),進(jìn)而總結(jié)了傳染病的發(fā)病機(jī)理、傳播途徑的相關(guān)知識(shí)和本文的研究意義。其次,陳述了涉及階段結(jié)構(gòu)和免疫逃避的傳染病動(dòng)力學(xué)模型中經(jīng)典“倉(cāng)室模型”的國(guó)內(nèi)外研究現(xiàn)狀,以及本文主要工作。最后,給出與傳染病模型動(dòng)力學(xué)研究相關(guān)的一些重要定義和定理。第二章,根據(jù)乙肝病毒性肝炎(HBV)的傳播規(guī)律和醫(yī)學(xué)現(xiàn)狀,新生兒不一定均是易感者,存在遺傳現(xiàn)象,建立了一個(gè)具有垂直傳染和連續(xù)預(yù)防接種的SIRS傳染病動(dòng)力學(xué)模型。為研究這種模型的漸近性態(tài),這里綜合運(yùn)用了 Routh-Hurwitz準(zhǔn)則、LaSalle不變集原理和廣義Dulac函數(shù)等方法,得到了關(guān)于無(wú)病平衡點(diǎn)和正平衡點(diǎn)全局漸近穩(wěn)定的充分條件。最后,選取合適的參數(shù)進(jìn)行數(shù)值模擬。第三章,由于在“倉(cāng)室模型”中,對(duì)疾病發(fā)生率的估計(jì)是傳染病流行趨勢(shì)預(yù)測(cè)和預(yù)防工作中最重要的。根據(jù)傳染病發(fā)生率的多樣性,考慮了易感者與染病者具有非線性發(fā)生率,建立了一個(gè)具有非線性發(fā)生率的SIRS傳染病動(dòng)力學(xué)模型。給出此傳染病動(dòng)力學(xué)模型的基本再生數(shù)R0,綜合利用Routh-Hurwitz定理、LaSalle不變集原理、微分方程軌道穩(wěn)定和復(fù)合矩陣的相關(guān)理論,得到無(wú)病平衡點(diǎn)和正平衡點(diǎn)全局穩(wěn)定的充分條件,進(jìn)而分析模型的生物學(xué)意義。最后,選取合適的參數(shù)進(jìn)行數(shù)值模擬。第四章,最新醫(yī)學(xué)研究數(shù)據(jù)表明,易感者接種乙肝疫苗后再次感染乙肝病毒的概率即免疫失去率,因易感者的年齡階段不同而出現(xiàn)差異。因此,基于不同年齡結(jié)構(gòu)免疫逃避的差異性,把易感人群分為幼年和成年兩個(gè)階段結(jié)構(gòu),考慮疾病在幼年和成年群體中均可傳播,且只考慮對(duì)幼年群體進(jìn)行連續(xù)預(yù)防接種,建立了一個(gè)具有階段結(jié)構(gòu)和免疫逃避的S1S2IR傳染病模型。為了研究這種模型的漸近性態(tài),我們給出模型的基本再生數(shù)R0,進(jìn)而利用Routh-Hurwitz準(zhǔn)則和微分方程比較定理,分別得到疾病消亡和最終成為地方病的充分條件。最后,選取合適的參數(shù)進(jìn)行數(shù)值模擬,并分析此傳染病模型的生物學(xué)意義。第五章,全文總結(jié)與展望。
[Abstract]:According to the "storeroom model" in the immune response of infectious disease model, this article aims at the phenomenon that the susceptible population will still be infected with hepatitis B virus after inoculation. Here we establish three SIRS epidemic dynamics models with phase structure and immune escape. Then the dynamic behavior of the model is studied and its biological significance is given. The full text is divided into five chapters. The first chapter, this chapter is the introduction of the full text. First, the development of infectious diseases and the basis of this paper are briefly introduced, and then the pathogenesis of infectious diseases, the relevant knowledge of transmission routes and the significance of this paper are summarized. Secondly, the research status of the classical "warehouse model" in infectious disease dynamics models involving phase structure and immune escape is presented, and the main work of this paper is also presented. Finally, some important definitions and theorems related to the dynamics of infectious disease models are given. In the second chapter, according to the law of (HBV) transmission and the current medical situation of hepatitis B virus hepatitis, the newborns are not all susceptible and have genetic phenomenon. A dynamic model of SIRS infectious disease with vertical transmission and continuous inoculation is established. In order to study the asymptotic behavior of the model, the Routh-Hurwitz criterion and the generalized Dulac function are used to obtain the sufficient conditions for the global asymptotic stability of the disease-free and positive equilibrium points. Finally, the appropriate parameters are selected for numerical simulation. In Chapter 3, the estimation of the incidence of disease is the most important in the prediction and prevention of epidemic trend of infectious diseases. According to the diversity of the incidence of infectious diseases, a dynamic model of SIRS infectious diseases with nonlinear incidence was established by considering the nonlinear incidence between susceptible and infected individuals. In this paper, the basic reproducing number R _ 0 of the dynamic model of infectious disease is given. The sufficient conditions for global stability of disease-free equilibrium point and positive equilibrium point are obtained by synthetically using Routh-Hurwitz theorem and LaSalle invariant set principle, the stability of differential equation orbit and the theory of compound matrix. Then the biological significance of the model is analyzed. Finally, the appropriate parameters are selected for numerical simulation. In the fourth chapter, the latest medical research data show that the probability of reinfection of hepatitis B virus after inoculating hepatitis B vaccine, that is, the rate of immune loss, varies with the age of susceptible person. Therefore, based on the difference of immune evasion in different age structure, the susceptible population was divided into two stages: early childhood and adult. A S1S2IR epidemic model with stage structure and immune escape was established. In order to study the asymptotic behavior of the model, we give the basic reproduction number R _ 0 of the model, and then by using the Routh-Hurwitz criterion and the comparison theorem of differential equations, we obtain the sufficient conditions for the disease to die out and finally become endemic. Finally, the appropriate parameters are selected for numerical simulation, and the biological significance of the epidemic model is analyzed. Chapter V, the full text summary and prospect.
【學(xué)位授予單位】：溫州大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 宋修朝;李建全;楊亞莉;;一類具有非線性發(fā)生率的SEIR傳染病模型的全局穩(wěn)定性分析[J];工程數(shù)學(xué)學(xué)報(bào);2016年02期

2 趙明;;基于SIRS傳染病模型的不同控制策略比較[J];北華大學(xué)學(xué)報(bào)(自然科學(xué)版);2015年05期

3 李冬梅;徐亞靜;韓春晶;;一類具有非線性接觸率的SEIR傳染病模型[J];哈爾濱理工大學(xué)學(xué)報(bào);2015年02期

4 張輝;徐文雄;李應(yīng)岐;;一類非線性SEIR傳染病模型的全局穩(wěn)定性[J];數(shù)學(xué)的實(shí)踐與認(rèn)識(shí);2015年04期

5 單秀麗;劉會(huì)民;;具有非線性傳染率和預(yù)防接種的SEIR傳染病模型的全局穩(wěn)定性[J];福州大學(xué)學(xué)報(bào)(自然科學(xué)版);2014年03期

6 楊洪;魏俊杰;;一類帶有非線性接觸率的SIR傳染病模型的穩(wěn)定性[J];高校應(yīng)用數(shù)學(xué)學(xué)報(bào)A輯;2014年01期

7 劉細(xì)憲;陳伯山;;一類SIR傳染病模型的全局穩(wěn)定性[J];湖北師范學(xué)院學(xué)報(bào)(自然科學(xué)版);2013年04期

8 葉志勇;豆中麗;馬文文;周鋒;;具有種群Logistic增長(zhǎng)的SIR模型的穩(wěn)定性和Hopf分支[J];生物數(shù)學(xué)學(xué)報(bào);2012年02期

9 于宇梅;張秋娟;;一類具有階段結(jié)構(gòu)的SIRS傳染病模型的穩(wěn)定性[J];大連交通大學(xué)學(xué)報(bào);2011年03期

10 李錄蘋(píng);賈建文;;一類具有飽和發(fā)生率的SEIR模型的全局穩(wěn)定性[J];數(shù)學(xué)的實(shí)踐與認(rèn)識(shí);2010年13期

相關(guān)博士學(xué)位論文 前1條

1 喬梅紅;乙肝病毒感染動(dòng)力學(xué)模型及其預(yù)防控制策略研究[D];華中科技大學(xué);2010年

相關(guān)碩士學(xué)位論文 前2條

1 王光菊;乙肝病毒的數(shù)學(xué)模型及定性分析[D];南華大學(xué);2012年

2 劉艷;一類具有年齡結(jié)構(gòu)的SIR傳染病模型分析[D];新疆大學(xué);2011年

，

本文編號(hào)：2174195