本文選題：閾值　切入點(diǎn)：非線性發(fā)生率　出處：《新疆大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：傳染病一直危害著人類的健康和生命,所以用數(shù)學(xué)模型研究傳染病的發(fā)病規(guī)律意義非常大.通過(guò)在確定模型上添加隨機(jī)擾動(dòng),從而建立了隨機(jī)傳染病模型.最近幾年許多的學(xué)者研究了隨機(jī)傳染病模型,他們主要討論了模型的持久性、滅絕性、解的正性以及平穩(wěn)分布.主要內(nèi)容可以概述如下:第一部分,我們首先介紹了隨機(jī)傳染病模型的生物背景及意義,隨后介紹了隨機(jī)傳染病模型的研究現(xiàn)狀,最后簡(jiǎn)述了本文的研究?jī)?nèi)容.第二部分,介紹了一些相關(guān)定義,給出了文中證明所用到的定義、記號(hào)、引理、定理等內(nèi)容.第三部分,在這一部分我們研究了一類具有非線性發(fā)生率的隨機(jī)SIVS傳染病模型,得到了閾值R0,并且建立了疾病的滅絕性和在均值意義下持久性的判別條件,即(?)1,則疾病依概率1是滅絕的,若(?)1,疾病依概率1在均值意義下是持久的.第四部分,我們討論了疾病的持久性和滅絕性.我們對(duì)傳輸率系數(shù)和因病死亡率進(jìn)行擾動(dòng),在先前的研究中,主要討論了疾病的滅絕性,但對(duì)于疾病的持久性很少進(jìn)行研究.我們給出了閾值R0s,若R0s1,則疾病依概率1是滅絕的,若R0s1,疾病依概率1在均值意義下是持續(xù)的.最后討論了在白噪聲不大時(shí),系統(tǒng)存在一個(gè)平穩(wěn)分布.第五部分,我們研究了一類具有非線性發(fā)生率和暫時(shí)免疫的隨機(jī)SIR傳染病模型.我們證明了,對(duì)任意的初始值,存在唯一的全局正解.并且建立了疾病滅絕和在均值意義下的持久性的條件:若(?)1,則疾病依概率1是滅絕的,若(?)1,疾病依概率1在均值意義下是持久的.第六部分,我們對(duì)本文的研究結(jié)果進(jìn)行了討論和總結(jié).
[Abstract]:Infectious diseases have been harmful to human health and life, so it is of great significance to use mathematical models to study the pathogenesis of infectious diseases. In recent years, many scholars have studied the stochastic infectious disease model, and they have mainly discussed the persistence and extinction of the model. The main contents can be summarized as follows: in the first part, we introduce the biological background and significance of stochastic infectious disease model, and then introduce the research status of stochastic infectious disease model. In the second part, some related definitions are introduced, and the definitions, notation, Lemma, theorems and so on used in the proof are given. In this part, we study a class of stochastic SIVS infectious disease models with nonlinear incidence, obtain threshold R0, and establish the criteria for disease extinction and persistence in the mean sense, I. e. If the disease is extinct according to the probability of 1? In part 4th, we discussed the persistence and extinction of disease. We perturbed the transmission rate coefficient and the disease mortality rate, in previous studies, This paper mainly discusses the extinction of disease, but seldom studies the persistence of disease. We give the threshold R0s, if R0s1, the disease is extinct according to probability 1. If R0s1, the disease depends on probability 1 is persistent in the mean value. Finally, it is discussed that the system has a stationary distribution. 5th, when white noise is small, In this paper, we study a class of stochastic SIR infectious disease models with nonlinear incidence and transient immunity. We prove that for arbitrary initial values, There is a unique global positive solution, and the condition of disease extinction and persistence in the mean sense is established. If the disease is extinct according to the probability of 1? Disease probability 1 is persistent in the sense of mean value. Part 6th, we discuss and summarize the research results of this paper.
【學(xué)位授予單位】：新疆大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175
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本文編號(hào)：1579314