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具有应急群体免疫的天花传播动力学模型研究

发表时间:2015-01-15  浏览量:1847  下载量:784
全部作者: 宋桃,张娟
作者单位: 华北电力大学数理学院
摘 要: 根据天花传播机理,建立在生物恐怖袭击背景下具有应急群体免疫的传播动力学模型。分析模型的渐近性态及接种比例对天花流行模式的影响,得到了模型的基本再生数,确定了各类平衡点存在的充分必要条件,分析得出了模型存在后项分支点,并利用LaSall不变集原理证明了无病平衡点的全局渐近稳定性。数值模拟结果直观地表明了接种比例对天花流行规律的影响。
关 键 词: 应用数学;天花;应急群体免疫;平衡点;基本再生数
Title: Study of transmission dynamics model of smallpox with emergency mass vaccination
Author: SONG Tao, ZHANG Juan
Organization: Department of Mathematics and Physics Departmeat, North China Electric Power University
Abstract: In this paper, the transmission dynamics model with emergency mass vaccination under the terrorism attack is established according to the mechanism of smallpox spread. The effect of vaccination rate on smallpox control and the asymptotic behavior are analysed and the basic reproductive number is found. Furthermore, the necessary and sufficient conditions of equilibria are obtained and the bifurcation point is exhibited. Using LaSalle invariant theory, the global asymptotical stability of the disease-free equilibrium is proved. The numerical simulation results intuitively show that the vaccination rate have influence on the smallpox epidemic.
Key words: applied mathematics; smallpox; emergency mass vaccination; equilibrium; basic reproductive number
发表期数: 2015年1月第1期
引用格式: 宋桃,张娟. 具有应急群体免疫的天花传播动力学模型研究[J]. 中国科技论文在线精品论文,2015,8(1):37-48.
 
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