传染病动力学模型中的地方病阈值
发布时间：2018-09-17 10:14
【摘要】：本文旨在介绍和研究传染病动力学模型中的地方病阈值。主要内容如下： 第一章，介绍了两个最基本的传染病动力学模型：SIR和SIS模型，并且在此基础上引出了常微分方程自治系统描述的传染病模型的基本再生数的定义及其计算。 第二章，提出了具有年龄结构和周期传染率的的SIS模型。把个体的一生分为未成年和成年两个阶段，只有未成年者会感染疾病。在模型中，，假设接触感染率为时间的周期函数，研究模型解的渐近行为，得到了疾病传播的阈值。
[Abstract]:The purpose of this paper is to introduce and study the threshold of endemic disease in epidemic dynamics model. The main contents are as follows: the first chapter introduces two basic infectious disease dynamics models: Sir and SIS. On this basis, the definition and calculation of the basic reproduction number of the infectious disease model described by the autonomous system of ordinary differential equations are introduced. In chapter 2, a SIS model with age structure and periodic infection rate is proposed. The life of an individual is divided into two stages: minor and adult. In the model, assuming that the contact infection rate is a periodic function of time, the asymptotic behavior of the solution of the model is studied, and the threshold of disease transmission is obtained.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2006
【分类号】：R181.3
本文编号：2245545
[Abstract]:The purpose of this paper is to introduce and study the threshold of endemic disease in epidemic dynamics model. The main contents are as follows: the first chapter introduces two basic infectious disease dynamics models: Sir and SIS. On this basis, the definition and calculation of the basic reproduction number of the infectious disease model described by the autonomous system of ordinary differential equations are introduced. In chapter 2, a SIS model with age structure and periodic infection rate is proposed. The life of an individual is divided into two stages: minor and adult. In the model, assuming that the contact infection rate is a periodic function of time, the asymptotic behavior of the solution of the model is studied, and the threshold of disease transmission is obtained.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2006
【分类号】：R181.3
【参考文献】
相关期刊论文 前1条
1 靳祯,马知恩;一类出身具有种群动力的非自治流行病模型[J];山西大学学报(自然科学版);2001年03期
本文编号：2245545
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