兰州大学机构库 >数学与统计学院
几乎周期环境下两类传染病模型的动力学行为研究
Alternative TitleThe Dynamics of Two Epidemic Models in an Almost Periodic Environment
崔灿
Thesis Advisor王宾国
2016-05-18
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword几乎周期系统 内宿主病毒模型 反应扩散 SIS 传染病模型 基本再生数 全局动力学行为
Abstract传染病的爆发是多种因素混合作用的结果, 其中个体随机运动导致的空间扩散和时间的非齐次性是影响疾病传播的重要因素. 在复杂的生活环境中, 传染病的发生和传播会受到季节性影响. 考虑季节性因素, 作者往往会认为传染病模型中影响疾病传播的系数都是具有相同周期的周期函数. 然而对于生活在复杂环境下的种群来说, 周期系统并不具有普遍性. 特别地, 当所研究模型中所涉及的周期系数的周期不具有整数公倍数时, 此时的模型就不是一个周期系统. 数学上, 可以引进更广泛的非自治—几乎周期系统. 本文将探究几乎周期环境下两类传染病模型的全局动力学性态. 考虑时间因素, 本文研究了复合药物治疗环境下的几乎周期内宿主病毒模型. 通过利用下一代生成算子的谱半径来定义模型的基本再生数, 然后建立了模型的全局动力学行为, 并用数值模拟来验证所建立的理论结果. 考虑到种群扩散和时间非齐次性等因素, 本文接着研究几乎周期环境下的反应扩散 SIS 传染病模型. 首先, 我们建立了抽象线性几乎抛物方程的相关理论. 其次, 通过利用下一代生成算子的谱半径来定义模型的基本再生数, 并且给出了它的计算公式和某些定量性质. 最后, 根据基本再生数得到模型全局动力学的一个阈值结论.
Other AbstractThe interaction of mixed factors leads to the outbreak of a infectious disease. Spatial diffusion and temporal heterogeneity are important factors that influence the spread of infectious diseases. Considering the seasonal factors, researchers tend to think the coefficients that affect the spread of diseases in epidemic models are periodic functions with the same period. For the population living in a complex environment, however, periodic system is not universal. Especially, if the periods of these coefficients functions have no common integer multiple, then the model is not a periodic system. Mathematically, we can treat such a model as an almost periodic system. This paper will explore the global dynamics of two epidemic models in an almost periodic environment. Considering the time factor, we first explore a within-host virus model with almost periodic multidrug therapy. First, we define the spectral radius of next generation operator as the basic reproduction number. Then, a threshold type result for uniform persistence and global extinction of the disease is obtained in terms of the basic reproduction number. Lastly, we illustrate the theoretical results by means of numerical simulations. Considering population diffusion and temporal heterogeneity, then we study a reaction-diffusion susceptible-infected-susceptible (SIS) epidemic model in an almost periodic environment. We first present the theory of abstract linear almost periodic parabolic equations. Next, by using the idea of the next generation operator, we establish the definition and the theories of the basic reproduction number, and obtain its computation formula. In particular, we get some quantitative properties for the basic reproduction number. Finally, we establish a threshold type result on the global dynamics in terms of the basic reproduction number.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225060
Collection数学与统计学院
Recommended Citation
GB/T 7714
崔灿. 几乎周期环境下两类传染病模型的动力学行为研究[D]. 兰州. 兰州大学,2016.
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