本文選題：隨機(jī)HIV傳染病模型　切入點(diǎn)：矩漸近穩(wěn)定　出處：《北方民族大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：由于當(dāng)今社會人員的流通性越來越廣泛,社會價值也呈現(xiàn)多樣性的趨勢,各種傳染疾病的傳播也越來越廣泛,導(dǎo)致越來越多學(xué)者致力于研究傳染病傳播過程和疾病感染抑制的機(jī)制,尤其是艾滋病.本文將隨機(jī)性引入傳染病模型,研究了在噪聲環(huán)境影響下的疾病傳播過程和疾病在個體中的滅絕條件,以及受Allee效應(yīng)影響下的體內(nèi)HIV病毒感染的過程.本文工作如下:首先,對一類隨機(jī)Human Immunodeficiency Virus(簡寫為HIV)模型進(jìn)行矩漸近穩(wěn)定分析.對隨機(jī)微分方程取集合平均,得到關(guān)于系統(tǒng)一階矩的微分方程,通過Routh-Hurwitz準(zhǔn)則得到一階矩漸近穩(wěn)定的充要條件.再利用伊藤公式,得到關(guān)于系統(tǒng)二階矩的微分方程,同理可得二階矩漸近穩(wěn)定的充要條件.其次,在Allee效應(yīng)影響的假設(shè)下,利用Ito公式、Lyapunov函數(shù)、Borel-Cantelli引理和鞅的不等式、鞅的大數(shù)定理進(jìn)一步證明了隨機(jī)HIV傳染病模型全局正解的存在唯一性,并得出了疾病滅絕的條件.并引入了一個具有混合雙線性發(fā)生率,劃分為五個群體的隨機(jī)HIV傳染病模型中證明了全局正解的存在唯一性,患病人群密度幾乎必然指數(shù)收斂和解的幾乎必然收斂的條件,對控制疫情提供了數(shù)據(jù)上的參考.最后,本文將方塊脈沖函數(shù)用于求解非線性隨機(jī)動力系統(tǒng).以隨機(jī)HIV傳染病模型為例,借助方塊脈沖函數(shù),給出了其近似非線性方程.
[Abstract]:As the circulation of social personnel is becoming more and more widespread, the social values are also showing a trend of diversity, and the spread of various infectious diseases is becoming more and more widespread. This has led more and more scholars to study the process of infectious disease transmission and the mechanism of disease infection inhibition, especially AIDS. The process of disease transmission under the influence of noise environment, the condition of disease extinction in individuals and the process of HIV virus infection in vivo under the influence of Allee effect are studied. The main work of this paper is as follows: first of all, The moment asymptotic stability of a class of stochastic Human Immunodeficiency virus model is analyzed. The first order moment differential equation of the system is obtained by taking the set average for the stochastic differential equation. By using the Routh-Hurwitz criterion, the necessary and sufficient conditions for the asymptotic stability of the first order moments are obtained. By using Ito's formula, the necessary and sufficient conditions for the asymptotic stability of the second order moments of the system are obtained by the same theory. Secondly, under the assumption of the influence of the Allee effect, The existence and uniqueness of the global positive solution of stochastic HIV infectious disease model are further proved by using the Ito formula and the inequality of Borel-Cantelli Lemma and martingale, and the large number theorem of martingale. The condition of disease extinction is obtained, and the existence and uniqueness of global positive solution are proved in a stochastic HIV infectious disease model with mixed bilinear incidence and divided into five populations. The density of the infected population is almost certain to converge exponentially and the condition of convergence is almost inevitable, which provides a data reference for the control of the epidemic situation. Finally, In this paper, the block impulse function is used to solve the nonlinear stochastic dynamical system. Taking the stochastic HIV epidemic model as an example, the approximate nonlinear equation is given by means of the block pulse function.
【學(xué)位授予單位】：北方民族大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

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