斑块环境下时滞周期传染病模型的阈值动力学行为研究

发布时间：2018-02-06 03:55

本文关键词： 基本再生数时滞传染病模型阈值动力学数值模拟　出处：《兰州大学》2017年硕士论文　论文类型：学位论文

【摘要】：传染病的研究一直都是一个重要的课题.传染病的爆发是很多因素交互影响的结果,而个体在斑块间扩散和时间的非齐次性是影响疾病传播的重要因素.时间的非齐次性则是由于季节性因素而引起的,因而周期传染病模型更能反映出疾病的传播特征.首先,本文借助“染病年龄”的概念推导了一个斑块环境中具有双线性发生率的带有时滞的时间非局部周期传染病模型.接着,本文以基本再生数R0为阈值研究了疾病的消亡持久性,结论表明当基本再生数R 1时,疾病是一致持久的,而当基本再生数R 1时,如果疾病的初始染病数目较小,疾病是趋于消亡的.特别地,如果易感类、潜伏类、感染类的扩散率相等,则当R0 1时疾病是趋于消亡的.其次,本文以两斑块情形为例,进行了数值模拟,结果显示疾病消亡持久的数值结果与理论结果相一致.同时,通过斑块之间有无扩散的比较,数值模拟表明斑块之间的扩散可能会导致疾病在两斑块流行,也可能会促使疾病在两斑块都消失.因此,是否控制斑块之间的成员流动对疾病的预防和控制起到至关重要的作用.最后,我们对本文做了一个简单的总结展望.
[Abstract]:The study of infectious diseases has always been an important subject. The outbreak of infectious diseases is the result of many factors. The spread of individual plaque and the inhomogeneity of time are the important factors that affect the spread of disease, and the inhomogeneity of time is caused by seasonal factors. Therefore, the periodic infectious disease model can better reflect the transmission characteristics of the disease. First of all. Based on the concept of "age of infection", a time-delay nonlocal periodic infectious disease model with bilinear incidence in plaque environment is derived. In this paper, the death persistence of disease is studied by using the basic regeneration number R0 as the threshold. It is concluded that when the basic regeneration number R 1:00, the disease is consistent and persistent, and when the basic regeneration number R 1:00. If the number of initial infections is small, the disease tends to die out. In particular, if the diffusivity of susceptible class, latent class and infected class is equal, then the disease tends to die out when R01. In this paper, we take two plaques as an example, and the results show that the numerical results of disease extinction are consistent with the theoretical results. At the same time, by comparing whether there is diffusion or not between plaques. Numerical simulations show that the spread between plaques may lead to disease epidemic in both plaques, or may cause disease to disappear in both plaques. Whether or not to control the flow of members between plaques plays an important role in disease prevention and control. Finally, we make a brief summary and prospect of this paper.
【学位授予单位】：兰州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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