具有连续接种免疫的SEIS模型和具有饱和接触率的SEIV模型的动力学分析

发布时间：2018-05-16 20:30

本文选题：传染病模型 + 饱和接触率　；参考：《昆明理工大学》2009年硕士论文

【摘要】：根据世界卫生组织最新的研究报告,传染病仍是危害人类生命和健康的第一杀手,人类依然面临着各种传染病长期而严竣的威胁。我们对传染病发病机理、流行规律、趋势预测的研究往往通过理论分析、模拟仿真等方法来进行。传染病动力学模型就是一种对传染病研究的重要方法。根据传染病的传播途径,这些模型通常被分为SI,SIR, SIS。SIRS,SEI,SEIR以及其他模式。以上的一些模式都没有考虑接种疫苗的情况,然而在实际生活中,接种疫苗是控制疾病的常用方法,例如乙型肝炎,麻疹和流行性感冒等等。因此在本文第二章研究了一类具有标准接触率的SEIV传染病模型：此模型存在两个平衡点,分别为无病平衡点和地方病平衡点。当基本再生数σ1时,无病平衡点是全局渐近稳定的,在这种情况下,地方病平衡点是不存在的。另一种情况下,当基本再生数σ1时,系统存在唯一的地方病平衡点,疾病一直持续存在,在一定的情况下,地方病平衡点是全局渐近稳定的。疾病的发生率是指每个单位时间内新增加的病例数目,疾病的接触率在关于传染病的数学模型的研究中起着非常重要的作用。蒂梅和卡斯蒂-查韦斯提出发生率的一般形式应该写成λ0C(N)S/NI,S和I分别表示在t时刻易感染者和患病者的数目,λ0表示当两个个体接触时在单位时间内疾病传播的可能性,C(N)是指单位时间内一个患者与他人接触的次数,第三章在第二章的基础上研究了带有饱和接触率的SEIV模型：此模型也存在两个平衡点,分别为无病平衡点和地方病平衡点。当基本再生数σ1时,无病平衡点是全局渐近稳定的,在这种情况下,地方病平衡点是不存在的。另一种情况下,当基本再生数σ1时,系统存在唯一的地方病平衡点,地方病平衡点是局部渐近稳定的。当没有发生因病死亡时,地方病平衡点是全局渐近稳定的。
[Abstract]:According to the latest research report of the World Health Organization, infectious diseases are still the first killer of human life and health, and human beings still face a long-term and serious threat of various infectious diseases. Our research on the pathogenesis, epidemic law and trend prediction of infectious diseases is often carried out by theoretical analysis, simulation and simulation. The kinetic model of infectious diseases is an important method for the study of infectious diseases. According to the route of transmission of infectious diseases, these models are usually classified as SISIRS, SIS.SIRSSEISEIR and other models. None of the above models take into account vaccinations, but in real life vaccination is a common method of disease control, such as hepatitis B, measles and influenza. In the second chapter of this paper, we study a class of SEIV infectious disease models with standard contact rate. There are two equilibrium points in this model, one is disease-free equilibrium point and the other is endemic equilibrium point. When the basic reproduction number 蟽 1, the disease-free equilibrium is globally asymptotically stable. In this case, the endemic equilibrium does not exist. In another case, when the basic reproduction number 蟽 1, the system has a unique endemic equilibrium, and the disease has been persistent. Under certain conditions, the endemic equilibrium is globally asymptotically stable. The incidence of disease refers to the number of new cases per unit of time, and the rate of disease exposure plays a very important role in the study of mathematical models of infectious diseases. Tiemer and Castil-Chavez suggested that the general form of incidence should be written as 位 0C / NS / NIS / NIS and I respectively to indicate the number of susceptible and infected persons at t time, and 位 0 to indicate the possibility of disease transmission per unit time when two individuals are in contact with each other. Sex is the number of times a patient is in contact with another person per unit of time. In chapter 3, based on the second chapter, we study the SEIV model with saturated contact rate. There are two equilibrium points in this model, one is disease-free equilibrium and the other is endemic equilibrium point. When the basic reproduction number 蟽 1, the disease-free equilibrium is globally asymptotically stable. In this case, the endemic equilibrium does not exist. In another case, when the basic reproducing number 蟽 1, the system has a unique endemic equilibrium, and the endemic equilibrium is locally asymptotically stable. When there is no death due to illness, the endemic equilibrium is globally asymptotically stable.
【学位授予单位】：昆明理工大学
【学位级别】：硕士
【学位授予年份】：2009
【分类号】：R186;O242.1

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