具有时滞的两类酗酒模型的研究
发布时间：2018-11-23 17:14
【摘要】：年轻人的酗酒行为引起了社会各界人士的广泛关注.众所周知,酗酒不仅危害个人身体健康,而且还会对社会导致一系列的负面影响,例如,暴力、反社会和犯罪行为.长期酗酒几乎对人体的各项器官都有损害,例如,肝硬化、胰腺炎、心脏病.因此,为了降低酗酒给年轻人带来的危害,研究酗酒的传播机制对控制酗酒的传播是具有重大意义的.近年来,主要是利用微分方程建立数学模型对酗酒进行研究,分析酗酒的传播并给出相应的控制措施.本文首先研究了一类分阶段结构且带有时滞影响的酗酒模型的动力学行为;其次,研究了一类具有复发和时滞影响的酗酒行为.第一章,给出了酗酒的定义、介绍了酗酒的发展历程、研究背景及意义.并给出了本文需要的一些预备知识.第二章,建立了一个分阶段结构及时滞影响的SAIRS酗酒模型,将酗酒人群分为轻度问题酗酒者和重度问题酗酒者两类,并考虑了恢复者向不饮酒或适度饮酒者转换的可能.本文的主要目的是研究时滞对于酗酒行为传播的影响,通过分析得到了基本再生数R_0,并证明了两个平衡点的稳定性.最终得到,基本再生数独立于时滞,但时滞会影响模型的稳定性.第三章,构建了一个具有复发和时滞影响的SIRS酗酒模型.主要目的是研究复发和时滞对酗酒行为传播的影响.通过分析的得到了基本再生数R_0,并证明了两个平衡点的稳定性.结果显示,复发率极大地影响了酗酒行为的传播,有效控制复发率可以减少酗酒人群的数量.
[Abstract]:The drinking behavior of young people has aroused the widespread concern of people from all walks of life. It is well known that alcohol abuse not only harms one's health, but also leads to a series of negative effects on society, such as violence, antisocial and criminal behavior. Chronic alcoholism can damage almost every organ of the body, such as cirrhosis, pancreatitis, and heart disease. Therefore, in order to reduce the harm of alcohol abuse to young people, it is of great significance to study the transmission mechanism of alcohol abuse to control the spread of alcohol abuse. In recent years, the mathematical model of differential equation is used to study alcoholism, and the transmission of alcoholism is analyzed and the corresponding control measures are given. In this paper, we first study the dynamic behavior of a class of alcoholism models with time-delay and staged structure, and then, we study the behavior of a class of alcoholics with the effects of recurrence and delay. In the first chapter, the definition of alcoholism is given, and the development, background and significance of alcoholism are introduced. Some preparatory knowledge needed in this paper is also given. In the second chapter, we establish a SAIRS alcoholism model with a phased structure and time-delay effects. The alcoholics are divided into two groups: mild problem drinkers and severe problem drinkers, and the possibility of transition from recovery to non-drinkers or moderate drinkers is considered. The main purpose of this paper is to study the influence of time delay on the propagation of alcoholism. By analyzing the basic regenerative number R _ S _ 0, we prove the stability of the two equilibrium points. Finally, it is obtained that the basic reproduction number is independent of the delay, but the delay will affect the stability of the model. In chapter 3, a SIRS alcoholism model with recurrent and delayed effects is constructed. The main purpose is to study the effects of relapse and delay on the spread of alcoholism. The basic reproducing number R _ S _ 0 is obtained by analysis, and the stability of the two equilibrium points is proved. The results showed that the recurrence rate greatly affected the spread of alcoholism, and the effective control of relapse rate could reduce the number of alcoholics.
【学位授予单位】：兰州理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
本文编号：2352197
[Abstract]:The drinking behavior of young people has aroused the widespread concern of people from all walks of life. It is well known that alcohol abuse not only harms one's health, but also leads to a series of negative effects on society, such as violence, antisocial and criminal behavior. Chronic alcoholism can damage almost every organ of the body, such as cirrhosis, pancreatitis, and heart disease. Therefore, in order to reduce the harm of alcohol abuse to young people, it is of great significance to study the transmission mechanism of alcohol abuse to control the spread of alcohol abuse. In recent years, the mathematical model of differential equation is used to study alcoholism, and the transmission of alcoholism is analyzed and the corresponding control measures are given. In this paper, we first study the dynamic behavior of a class of alcoholism models with time-delay and staged structure, and then, we study the behavior of a class of alcoholics with the effects of recurrence and delay. In the first chapter, the definition of alcoholism is given, and the development, background and significance of alcoholism are introduced. Some preparatory knowledge needed in this paper is also given. In the second chapter, we establish a SAIRS alcoholism model with a phased structure and time-delay effects. The alcoholics are divided into two groups: mild problem drinkers and severe problem drinkers, and the possibility of transition from recovery to non-drinkers or moderate drinkers is considered. The main purpose of this paper is to study the influence of time delay on the propagation of alcoholism. By analyzing the basic regenerative number R _ S _ 0, we prove the stability of the two equilibrium points. Finally, it is obtained that the basic reproduction number is independent of the delay, but the delay will affect the stability of the model. In chapter 3, a SIRS alcoholism model with recurrent and delayed effects is constructed. The main purpose is to study the effects of relapse and delay on the spread of alcoholism. The basic reproducing number R _ S _ 0 is obtained by analysis, and the stability of the two equilibrium points is proved. The results showed that the recurrence rate greatly affected the spread of alcoholism, and the effective control of relapse rate could reduce the number of alcoholics.
【学位授予单位】：兰州理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
【参考文献】
相关硕士学位论文 前5条
1 王彦彦;复杂网络中几类酗酒模型的研究[D];兰州理工大学;2016年
2 刘映平;复杂网络上具有阶段结构和复发的酗酒模型研究[D];兰州理工大学;2016年
3 刘云峰;两类具有饱和时滞发生率的传染病模型的研究[D];山西师范大学;2014年
4 宋娜娜;具有阶段结构的酗酒模型的全局稳定性[D];兰州理工大学;2013年
5 朱承澄;具有复发的酗酒与吸烟模型的全局稳定性[D];兰州理工大学;2013年
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