【摘要】：年輕人的酗酒行為引起了社會各界人士的廣泛關(guān)注.眾所周知,酗酒不僅危害個人身體健康,而且還會對社會導(dǎo)致一系列的負面影響,例如,暴力、反社會和犯罪行為.長期酗酒幾乎對人體的各項器官都有損害,例如,肝硬化、胰腺炎、心臟病.因此,為了降低酗酒給年輕人帶來的危害,研究酗酒的傳播機制對控制酗酒的傳播是具有重大意義的.近年來,主要是利用微分方程建立數(shù)學(xué)模型對酗酒進行研究,分析酗酒的傳播并給出相應(yīng)的控制措施.本文首先研究了一類分階段結(jié)構(gòu)且?guī)в袝r滯影響的酗酒模型的動力學(xué)行為;其次,研究了一類具有復(fù)發(fā)和時滯影響的酗酒行為.第一章,給出了酗酒的定義、介紹了酗酒的發(fā)展歷程、研究背景及意義.并給出了本文需要的一些預(yù)備知識.第二章,建立了一個分階段結(jié)構(gòu)及時滯影響的SAIRS酗酒模型,將酗酒人群分為輕度問題酗酒者和重度問題酗酒者兩類,并考慮了恢復(fù)者向不飲酒或適度飲酒者轉(zhuǎn)換的可能.本文的主要目的是研究時滯對于酗酒行為傳播的影響,通過分析得到了基本再生數(shù)R_0,并證明了兩個平衡點的穩(wěn)定性.最終得到,基本再生數(shù)獨立于時滯,但時滯會影響模型的穩(wěn)定性.第三章,構(gòu)建了一個具有復(fù)發(fā)和時滯影響的SIRS酗酒模型.主要目的是研究復(fù)發(fā)和時滯對酗酒行為傳播的影響.通過分析的得到了基本再生數(shù)R_0,并證明了兩個平衡點的穩(wěn)定性.結(jié)果顯示,復(fù)發(fā)率極大地影響了酗酒行為的傳播,有效控制復(fù)發(fā)率可以減少酗酒人群的數(shù)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.
【學(xué)位授予單位】：蘭州理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

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本文編號：2352197