网络上具有传播媒介的SIS模型分析

发布时间：2018-06-28 18:22

本文选题：SIS模型 + 传播媒介　；参考：《山西大学》2017年硕士论文

【摘要】：传染病模型的研究为疾病的控制提供了理论依据和现实指导,具有重要的科研价值和现实意义.本文以疟疾和黄热病的染病机制为背景,建立了网络上具有传播媒介的SIS模型,使模型更贴近现实.第一章,介绍了从数学建模角度研究传染病的必要性及具有传播媒介的SIS模型的研究进程,并简单概述本文工作.第二章,根据疟疾的传播机制,基于无标度网络建立了具有多种传播媒介和多个染病阶段的SIS模型其中(?)表示一个易感者发出的所有边中的其中一条与染病者相连的概率,θ(t)=1/k(?)kP(k)Ik(t),根据理论推导计算出模型的传播阈值λc,并证明当R0 1时,无病平衡点全局渐近稳定,当R0 1时地方病平衡点全局吸引,最后通过相应的数值仿真得到的结果与上述结论保持一致.第三章,在第二章模型的基础上,注意到病毒在传播媒介上存在潜伏期,故考虑时滞对传播媒介的影响,并建立下面的模型其中θ(t)=4/k(?)φ(i)p(i)Ii(t).根据理论推导得到了疾病的传播阈值,最后通过进行相应的数值仿真直观地反映各参数在疾病传播过程中的影响.第四章,总结本文研究得到的结果,并就后续工作提出自己的看法.
[Abstract]:The study of infectious disease model provides theoretical basis and practical guidance for disease control, and has important scientific research value and practical significance. Based on the infection mechanism of malaria and yellow fever, an SIS model with transmission vector on the network was established to make the model closer to reality. In the first chapter, the necessity of studying infectious diseases from the angle of mathematical modeling and the research process of SIS model with media are introduced, and the work of this paper is briefly summarized. In the second chapter, according to the transmission mechanism of malaria, an SIS model with multiple vectors and stages of infection is established based on scale-free network. To represent the probability that one of the edges issued by a susceptible person is connected to the infected person, the propagation threshold 位 _ c of the model is derived from the胃 (t) _ 1 / k (?) KP (k) I _ k (t), and it is proved that the disease-free equilibrium is globally asymptotically stable when R _ (0.1). When R _ (01) is the global attraction of endemic equilibrium, the results obtained by corresponding numerical simulation are consistent with the above conclusions. In the third chapter, based on the model in chapter 2, the latent period of virus in the media is noticed, so the influence of delay on the media is considered, and the following model is established, in which 胃 (t) 4 / k (?) 蠁 (i) p (i) I I (t). According to the theoretical derivation, the disease transmission threshold is obtained, and the effect of each parameter on the disease transmission is reflected intuitively by the corresponding numerical simulation. The fourth chapter summarizes the results of this study and puts forward its own views on the follow-up work.
【学位授予单位】：山西大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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