一类艾滋病传播动力学模型的分析与应用 Alternative Title The Analysis and Application of a Kind of HIV/AIDS Transmission Dynamics Model 苏莉莉 Thesis Advisor 李维德 2018-03-31 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword HIV/AIDS 动力学模型 基本再生数 稳定性分析 敏感性分析 Abstract 艾滋病(Acquired Immune Deficiency Syndrome，AIDS)，也称为获得性免疫综合症，是由人类免疫缺陷病毒(Human immunodeficiency virus，HIV)引起的一种传染性疾病。HIV/AIDS是一种严重影响人类生活和社会发展的疾病，因此研究HIV/AIDS的传播规律有非常重要的意义。本文新建了一类HIV/AIDS传播动力学模型，并应用该模型研究了我国HIV/AIDS的传播情况。首先，根据HIV/AIDS的传播机理构建了一类具有治疗过程的微分动力系统模型，分析了系统平衡点存在的性质，讨论了无病平衡点和地方病平衡点存在的稳定性条件，计算了基本再生数的值。当基本再生数小于1时，无病平衡点全局渐进稳定；当基本再生数大于1时，地方病平衡点全局渐进稳定，并用数值模拟验证了模型分析的结果。其次，根据中国疾病预防控制中心报告的数据(2004年1月至2015年12月)，近似的估计了模型的参数值，计算了我国HIV/AIDS的基本再生数。本文利用拉丁超立方体抽样(Latin hypercube sampling，LHS)技术和偏等级相关系数(Partial rank correlation coefficient，PRCC)讨论了影响基本再生数的显著性因素，且对HIV/AIDS的感染变量进行了多参数时变敏感性分析。最后，应用本文建立的模型模拟预测我国HIV/AIDS流行的状况，经计算所得基本再生数为1.20727 > 1，该结果显示艾滋病在我国已经逐渐形成地方病。模型模拟的结果也表明治疗对预防HIV/AIDS的传播有非常重要的作用和意义。因此，建议对感染HIV/AIDS的患者及时治疗，同时减少与HIV/AIDS感染者的接触并做好预防措施。 Other Abstract Acquired Immune Deficiency Syndrome (AIDS) is also known as Acquired Immune Syndrome. AIDS is a contagious disease caused by Human Immunodeficiency Virus(HIV). HIV/AIDS is an infectious disease that severely affects human life and social development. Therefore, it is of great significance to study the transmission dynamics of HIV/AIDS. This paper builds a new type of HIV/AIDS transmission dynamics model and applies the model to study the transmission trend of HIV/AIDS in China. Firstly, based on the mechanism of the compartment transmission of HIV/AIDS, a differential dynamic system model with the treatment process is build. The properties of equilibrium point and the stability conditions of disease-free equilibrium and endemic disease equilibrium are discussed. Then the basic reproduction number is calculated. When the basic reproduction number is less than 1, the disease-free equilibrium is globally asymptotic stable; When the basic reproduction number is more than 1, the endemic disease equilibrium is globally asymptotic stable. And the results of theoretical analysis are verified by numerical simulation. Secondly, according to the data reported by the Chinese Center for Disease Control and Prevention (January 2004 to December 2015), the parameter values of the model were estimated and the basic reproduction number  of HIV/AIDS in China was calculated. Then, using Latin Hypercube Sampling (LHS) technology and Partial Rank Correlation Coefficient (PRCC), the significant factors influencing the basic reproduction number R-0,and the time-varying sensitivity of infection variables of HIV/AIDS with multiple parameters are analyzed. Finally, the model established in this paper is used to simulate the trend of HIV/AIDS epidemic in China, and the reproduction number is calculated as 1.20727 and more than 1, which indicates that HIV/AIDS has gradually become an endemic in China. Simulation results also show that treatment is very important and meaningful in preventing HIV/AIDS transmission. Therefore, it is recommended to treat patients with HIV/AIDS timely and to reduce the contact with HIV/AIDS patients and take effective preventive measures for AIDS defence. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/224529 Collection 数学与统计学院 Recommended CitationGB/T 7714 苏莉莉. 一类艾滋病传播动力学模型的分析与应用[D]. 兰州. 兰州大学,2018.
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