几类随机传染病模型的渐近行为

发布时间：2018-04-29 14:27

本文选题：随机传染病系统 + 带Lévy跳　；参考：《南昌大学》2016年硕士论文

【摘要】：在自然界生态系统中,随处可见各种随机干扰.在确定性传染病模型中加入随机干扰的影响,能够更贴近实际的传染病系统.本文主要讨论了传染病模型受到白噪声的干扰以及带Lévy跳干扰项时系统的渐近行为,具体讨论内容依次如下:第1章主要介绍了近年来传染病模型的研究概况,同时也概括出了本文的主要工作.第2章研究了一类带Lévy跳的随机SIR传染病模型和随机SEIR传染病模型的渐近行为.先证明了系统全局正解的存在唯一性,再讨论了带Lévy跳的随机系统解在确定性模型的平衡点附近的行为,最后得到了随机系统的灭绝性.第3章讨论了一类具有两种传染病的非线性随机SIS传染病模型.运用Doob's鞅不等式,Burkholder-Davis-Gundy不等式及Borel-Cantelli引理等,分别得到了随机传染病系统中两种疾病的灭绝性与平均持久性的阈值.并用数学软件MATLAB做了相应的数值模拟.第4章总结了本文所研究的内容和主要结论,并对进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.
【学位授予单位】：南昌大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O175

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