本文關鍵詞： 肺結核 快慢進程 不完全免疫力 預防性治療 后向分支 無病平衡點和地方病平衡點 局部漸近穩(wěn)定性　出處：《華北電力大學》2013年碩士論文　論文類型：學位論文

【摘要】：肺結核是由結核桿菌引起的慢性呼吸道傳染病,是我國發(fā)病人數(shù)及死亡人數(shù)最多的重大傳染疾病之一,也是世界共同關注的疾病之一,世界衛(wèi)生組織已經(jīng)將肺結核病列為需要重點控制的三種傳染病之一。對結核桿菌攜帶者的預防性治療不僅可大大降低病菌攜帶者的發(fā)病幾率,而且可以有效降低結核病患者的傳染能力、減輕結核病患者發(fā)病的癥狀,因此預防性治療對肺結核的防治有著重要意義。 為了分析在不同的情況下預防性治療對肺結核傳播的影響,本文根據(jù)肺結核的傳播機理及防治策略,建立了三個考慮不同因素的具有預防性治療的肺結核傳播動力學模型：僅考慮肺結核快慢進程現(xiàn)象而不考慮獲得性免疫力的不完全性的模型；僅考慮不完全性獲得性免疫力而不考慮快慢進程機制的模型以及兩個因素均考慮的復雜模型。對所建模型,我們均在全參數(shù)空間分析了模型的動力學性態(tài),得到了無病平衡點及地方病平衡點存在和局部漸近穩(wěn)定的充分必要條件,確定了決定疾病滅絕與否的閾值也即模型的基本再生數(shù)以及各種分支出現(xiàn)的充要條件和分支點,進而確定了模型具有的豐富而復雜的動力學性質(zhì)。另外,本文還基于不同的預防性治療率,對模型的動力學性態(tài)進行了數(shù)值模擬,數(shù)值模擬的結果不僅驗證了理論分析的正確性,而且直觀地展示了預防性治療等因素對各時段染病者人數(shù)以及平衡狀態(tài)的影響。 特別地,在第二章證明了考慮肺結核的快慢進程機制而不考慮免疫力的不完全性的模型與不考慮預防性治療的同類模型的動力學性態(tài)類似,都存在后向分支。而這一結果說明即使基本再生數(shù)小于1,疾病也可能流行。而對于考慮不完全免疫力的模型,無論是否考慮肺結核的快慢進程現(xiàn)象,在第三章和第四章,我們均證明了本文所建模型的動力學性態(tài)都與不具有預防性治療的同類模型非常不同：本文的模型不僅存在后向分支,而且在基本再生數(shù)大于1時存在兩個穩(wěn)定和一個不穩(wěn)定地方病平衡點,這也就是說疾病的流行不僅依賴染病的初始狀態(tài),還敏感地依賴潛伏者的預防性治療成功率和易感者的有效接種率。這些結果為我們在醫(yī)療資源和經(jīng)濟條件有限的情況下,如何根據(jù)不同地區(qū)的染病情況確定合適的預防性治療率和疫苗接種率達到防治目標提供了可供參考的依據(jù)。
[Abstract]:Pulmonary tuberculosis is a chronic respiratory infectious disease caused by Mycobacterium tuberculosis. It is one of the most serious infectious diseases in China and one of the diseases of common concern in the world. The World Health Organization has listed tuberculosis as one of the three major infectious diseases that need to be controlled. Preventive treatment of TB carriers can not only significantly reduce the incidence of TB carriers. Moreover, it can effectively reduce the infectious ability of TB patients and alleviate the symptoms of TB patients. Therefore, preventive treatment is of great significance to the prevention and treatment of tuberculosis. In order to analyze the influence of preventive treatment on the transmission of pulmonary tuberculosis under different conditions, according to the transmission mechanism and prevention strategy of pulmonary tuberculosis, Three dynamic models of pulmonary tuberculosis transmission with prophylactic treatment were established considering different factors: the incomplete model of acquired immunity without considering the phenomenon of rapid and slow progress of pulmonary tuberculosis; The model of incomplete acquired immunity without considering the mechanism of fast and slow process and the complex model of both factors are considered. For the established model, the dynamic behavior of the model is analyzed in the full parameter space. The sufficient and necessary conditions for the existence and local asymptotic stability of disease-free equilibrium and endemic equilibrium are obtained. The threshold of disease extinction is determined, that is, the basic regenerative number of the model, the necessary and sufficient conditions for the occurrence of various branches and the bifurcation points. Furthermore, the rich and complex dynamic properties of the model are determined. In addition, the dynamic behavior of the model is numerically simulated based on the different rates of preventive treatment. The results of numerical simulation not only verify the correctness of theoretical analysis, but also show directly the influence of preventive treatment on the number of infected persons and the equilibrium state of each period of time. In particular, in chapter II, we prove that models that consider the mechanism of pulmonary tuberculosis's rapid and slow progression without considering the imperfections of immunity are similar to the dynamics of similar models that do not consider preventive treatment. The results show that disease can be prevalent even if the number of basic regenerations is less than 1. For models that consider incomplete immunity, whether or not the rapid progression of tuberculosis is taken into account, chapters 3 and 4th, We all prove that the kinetic behavior of the model is very different from that of the similar model without preventive therapy: the model in this paper has not only backward branching, And there are two stable and one unstable endemic equilibrium points when the basic regeneration number is greater than 1:00, which means that the prevalence of the disease depends not only on the initial condition of the disease, but also on the initial condition of the disease. It is also sensitive to the success rate of preventive treatment of the sleeper and the effective coverage rate of the susceptible. These results provide us with limited medical resources and financial conditions. How to determine the appropriate preventive treatment rate and vaccine vaccination rate according to the infection conditions in different areas provides a reference basis for the prevention and control of the disease.
【學位授予單位】：華北電力大學
【學位級別】：碩士
【學位授予年份】：2013
【分類號】：R521;O175

【參考文獻】

相關期刊論文 前6條

1 楊建安,闞曉宏;肺結核病發(fā)病影響因素流行病學調(diào)查研究[J];安徽醫(yī)學;2002年04期

2 王峰,張娟,馬知恩;具有線性免疫響應的HIV-TB共感染模型[J];工程數(shù)學學報;2003年06期

3 余蘭萍,鄭洲順,林鋒;具有年齡結構的結構病模型的研究[J];數(shù)學理論與應用;2004年04期

4 辛梅平;孫業(yè)建;李明霞;祁培春;;結核感染的異煙肼預防性治療[J];青島醫(yī)藥衛(wèi)生;2009年04期

5 張少茹;顏虹;李天來;張宏偉;王娣妙;;人類免疫缺陷病毒(HIV)與結核桿菌(TB)雙重感染的研究進展[J];西北醫(yī)學教育;2007年06期

6 王黎霞，，施洪生，劉勝安;我國結核病流行病學模型及疫情態(tài)勢淺析[J];中國衛(wèi)生統(tǒng)計;1994年04期

本文編號：1532457