几类新型传染病模型动力学分析及其研究

发布时间：2018-07-01 14:26

  本文选题：传染病模型 + 输入输出　； 参考：《兰州交通大学》2015年硕士论文

【摘要】：传染病作为人类生命的第一杀手,一直以来是世界各国人民高度关注的问题.近年来,由于各方面的原因各种各样的新型传染病相用而现,肆虐的吞噬者人类的生命.严重危害着人类的健康,影响着人们的生产生活和经济的发展.因此,揭示传染病的发展规律将有助于预测传染病的发展趋势,为有关部门制定传染病的预防与控制策略提供有效的科学依据,使人们远离疾病的困扰.目前,利用动力学方法建立传染病的相关数学模型,并对其模型从定性和定量的两方面进行动力学的分析与研究,从而来揭示传染病的流行规律,已经成为了一种趋势,备受国内为众多学者的广泛关注,在这方面研究的丰硕成果已大量存在.本论文针对几类新型传染病建立相应的数学模型,分析并研究了其动力学行为即自治系统平衡点的局部和全局的渐进稳定性,非自治系统解的正性和周期解的存在性和稳定性以及疾病的持久性、灭绝性等主要内容如下：(1)讨论了一类具有垂直传染的sIQR传染病模型,得到了传染病流行与否的阈值条件R01*,当R01*≤1时,无病平衡点是全局稳定的；当R01*1时,无病平衡点E0是不稳定的；当R*01=min{R*01,R*02,R*02,1}时,全局渐进稳定的是地方病平衡点E1和E2.(2)讨论了带有人口输入和人口输出平均分配的SEIR传染病的数学模型,通过分析求得基本再生数R0,当R01时,无病平衡点E0是全局稳定的,即无论疾病初始状态如何,最终会走向灭亡.当R01时,地方病平衡点唯一存在且是全局渐进稳定的,即疾病在人群中持续不断的流行,最终形成地方性传染病.(3)讨论了带有人口输入和人口输出的非自治情形下的SEIR传染病的数学模型,解的正性用反正法证得,同时疾病的持久性及灭绝性的充要条件被求得,以及当模型中的系数函数均为时间t的周期函数时,通过构造Lyapunov函数并对其求右导数的方法,得到了周期系统对应的周期解的存在性及稳定性的充分条件.
[Abstract]:Infectious disease, as the first killer of human life, has always been a high concern of people all over the world. In recent years, various kinds of new infectious diseases have been used for various reasons, which engulfs human life. Serious harm to human health, affecting people's production and life and economic development. Therefore, revealing the development law of infectious diseases will help to predict the development trend of infectious diseases, provide effective scientific basis for the departments concerned to formulate the prevention and control strategies of infectious diseases, and make people away from the troubles of diseases. At present, it has become a trend to establish relevant mathematical models of infectious diseases by using kinetic methods, and to analyze and study the dynamics of infectious diseases from both qualitative and quantitative aspects, so as to reveal the epidemic law of infectious diseases. It has been paid much attention by many scholars in our country, and there have been a lot of achievements in this field. In this paper, the corresponding mathematical models of several new infectious diseases are established, and the dynamic behavior of these models is analyzed and studied, that is, the local and global asymptotic stability of the equilibrium points of autonomous systems. The main contents of the positive and periodic solutions of nonautonomous systems, as well as the persistence and extinction of diseases, are as follows: (1) A class of sIQR infectious disease models with vertical transmission are discussed. The threshold condition of epidemic or not is obtained. When R01 * 鈮，

本文编号：2088072