流感模型的数据模拟和动力学分析  

Data Simulation and Dynamic Analysis of the Influenza Model

作　　者：吴荣杰 冯光庭 张兴安[1] 方奕乐 WU Rong-jie;FENG Guang-ting;ZHANG Xing-an;FANG yi-le(School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;School of Mathematics and Statistics, Hubei University of Education, Wuhan 430205, China;School of Mechatronic Engineering and Automation, Wuchang Shouyi University, Wuhan 430064, China)

机构地区：[1]华中师范大学数学与统计学学院,湖北武汉430079 [2]湖北第二师范学院数学与经济学院,湖北武汉430205 [3]武昌首义学院机电自动化学院,湖北武汉430064

出　　处：《数学的实践与认识》2018年第8期143-152,共10页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11071275,11228104,11371161);湖北省自然科学基金(2013CFB013)

摘　　要：利用常微分方程定性和稳定性理论、计算机工具建立并研究了没有疫苗和带有疫苗的流感模型.根据中国疾控中心的数据,利用MATLAB进行参数模拟,得到了流感基本再生数的取值范围,并对疫苗的年生产量做出了估计;同时,求出了模型的无病平衡点和地方病平衡点,证明了无病平衡点当基本再生数小于1时是全局渐进稳定的、地方病平衡点存在时是局部稳定的.In this paper, by using quMitative theory of ordinary differential equations and stability theory and computer tools, we establish and study two mathematical models of influenza with vaccine and without vaccine. According to data from the Chinese Center for Disease Control and Prevention, the parameters of the models was simulated by using MATLAB to obtain the range of the basic reproduction number of influenza, then we estimate the annual production of vaccines. Meanwhile we calculate the disease-free equilibrium and endemic equilibrium point in the model. The disease-free equilibrium is globally asymptotically stable when the basic reproduction number is less than 1. The endemic equilibrium, when it exists, is shown to be locally stable.

关 键 词：流行性感冒 数据模拟 基本再生数 平衡点 全局渐进稳定 

分 类 号：O175[理学—数学]