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  本文選題：隨機傳染病系統(tǒng) + 帶Lévy跳��； 參考：《南昌大學(xué)》2016年碩士論文

【摘要】：在自然界生態(tài)系統(tǒng)中,隨處可見各種隨機干擾.在確定性傳染病模型中加入隨機干擾的影響,能夠更貼近實際的傳染病系統(tǒng).本文主要討論了傳染病模型受到白噪聲的干擾以及帶Lévy跳干擾項時系統(tǒng)的漸近行為,具體討論內(nèi)容依次如下:第1章主要介紹了近年來傳染病模型的研究概況,同時也概括出了本文的主要工作.第2章研究了一類帶Lévy跳的隨機SIR傳染病模型和隨機SEIR傳染病模型的漸近行為.先證明了系統(tǒng)全局正解的存在唯一性,再討論了帶Lévy跳的隨機系統(tǒng)解在確定性模型的平衡點附近的行為,最后得到了隨機系統(tǒng)的滅絕性.第3章討論了一類具有兩種傳染病的非線性隨機SIS傳染病模型.運用Doob's鞅不等式,Burkholder-Davis-Gundy不等式及Borel-Cantelli引理等,分別得到了隨機傳染病系統(tǒng)中兩種疾病的滅絕性與平均持久性的閾值.并用數(shù)學(xué)軟件MATLAB做了相應(yīng)的數(shù)值模擬.第4章總結(jié)了本文所研究的內(nèi)容和主要結(jié)論,并對進一步的研究加以展望.
[Abstract]:In natural ecosystems, a variety of random disturbances can be found everywhere. The effect of random interference can be added to the deterministic infectious disease model, which can be closer to the real infectious disease system. In this paper, we mainly discuss the interference of white noise and the asymptotic behavior of the system with L 茅 vy jump interference. The main contents are as follows: chapter 1 mainly introduces the research situation of infectious disease model in recent years. At the same time, the main work of this paper is summarized. In chapter 2, we study the asymptotic behavior of a class of stochastic SIR infectious disease model with L 茅 vy jump and stochastic SEIR epidemic model. The existence and uniqueness of the global positive solution of the system are first proved, then the behavior of the solution of the stochastic system with L 茅 vy jump near the equilibrium point of the deterministic model is discussed. Finally, the extinction of the stochastic system is obtained. Chapter 3 discusses a class of nonlinear stochastic SIS infectious disease models with two infectious diseases. By using Doob's martingale inequality and Burkholder-Davis-Gundy inequality and Borel-Cantelli Lemma, the threshold of extinction and mean persistence of two diseases in stochastic infectious disease systems are obtained respectively. The corresponding numerical simulation is done with the mathematical software MATLAB. Chapter 4 summarizes the contents and main conclusions of this paper, and looks forward to further research.
【學(xué)位授予單位】：南昌大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：O175

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本文編號：1820320