考虑预防性治疗的肺结核动力学模型研究

发布时间：2018-02-25 01:18

本文关键词： 肺结核快慢进程不完全免疫力预防性治疗后向分支无病平衡点和地方病平衡点局部渐近稳定性　出处：《华北电力大学》2013年硕士论文　论文类型：学位论文

【摘要】：肺结核是由结核杆菌引起的慢性呼吸道传染病,是我国发病人数及死亡人数最多的重大传染疾病之一,也是世界共同关注的疾病之一,世界卫生组织已经将肺结核病列为需要重点控制的三种传染病之一。对结核杆菌携带者的预防性治疗不仅可大大降低病菌携带者的发病几率,而且可以有效降低结核病患者的传染能力、减轻结核病患者发病的症状,因此预防性治疗对肺结核的防治有着重要意义。为了分析在不同的情况下预防性治疗对肺结核传播的影响,本文根据肺结核的传播机理及防治策略,建立了三个考虑不同因素的具有预防性治疗的肺结核传播动力学模型：仅考虑肺结核快慢进程现象而不考虑获得性免疫力的不完全性的模型；仅考虑不完全性获得性免疫力而不考虑快慢进程机制的模型以及两个因素均考虑的复杂模型。对所建模型,我们均在全参数空间分析了模型的动力学性态,得到了无病平衡点及地方病平衡点存在和局部渐近稳定的充分必要条件,确定了决定疾病灭绝与否的阈值也即模型的基本再生数以及各种分支出现的充要条件和分支点,进而确定了模型具有的丰富而复杂的动力学性质。另外,本文还基于不同的预防性治疗率,对模型的动力学性态进行了数值模拟,数值模拟的结果不仅验证了理论分析的正确性,而且直观地展示了预防性治疗等因素对各时段染病者人数以及平衡状态的影响。特别地,在第二章证明了考虑肺结核的快慢进程机制而不考虑免疫力的不完全性的模型与不考虑预防性治疗的同类模型的动力学性态类似,都存在后向分支。而这一结果说明即使基本再生数小于1,疾病也可能流行。而对于考虑不完全免疫力的模型,无论是否考虑肺结核的快慢进程现象,在第三章和第四章,我们均证明了本文所建模型的动力学性态都与不具有预防性治疗的同类模型非常不同：本文的模型不仅存在后向分支,而且在基本再生数大于1时存在两个稳定和一个不稳定地方病平衡点,这也就是说疾病的流行不仅依赖染病的初始状态,还敏感地依赖潜伏者的预防性治疗成功率和易感者的有效接种率。这些结果为我们在医疗资源和经济条件有限的情况下,如何根据不同地区的染病情况确定合适的预防性治疗率和疫苗接种率达到防治目标提供了可供参考的依据。
[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.
【学位授予单位】：华北电力大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：R521;O175

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