HIV在中国的动力学模型的稳定性研究  

Study on the stability of dynamic model of HIV in China

作　　者：申笑然 薛亚奎[1] 

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《高师理科学刊》2015年第10期6-16,共11页Journal of Science of Teachers＇College and University

基　　金：国家自然科学基金资助项目(10901145);山西省自然科学基金项目(2009011005-1;2012011002-1);山西省高等院校中青年学科带头人项目

摘　　要：针对毒品吸毒注射者(injecting drug users,简称IDUs),女性性工作者(female sex workers,简称FSWs)及其顾客(clients of female sex workers,简称CFSWs),研究有关艾滋病病毒在中国这些人群中的传播动力学的数学模型.建立4种平衡存在的状态,提出并证明局部渐进稳定性和全局渐进稳定性.模拟实验结果与中国卫生部报道的艾滋病病毒数据相吻合,预测出了艾滋病病毒的传染趋势,并预估出了其基本的再生数量.另外,也对艾滋病病毒的防控措施进行了分析讨论.The groups of injecting drug users （ IDUs ）, female sex workers （ FSWs ） and clients of female sex workers （ CFSWs ） was focused on. A mathematical model about HIV to study the transmission dynamics of those groups in China was proposed. The conditions for the existence of four equilibria was established, and the conditions for the local asymptotically stability and global asymptotically stability of these equilibria was proposed and proved. The simulations conform to the HIV data which are reported by the Chinese ministry of health. Then the trend of ttIV infection was predicted and the basic reproduction number was estimated. In addition, the controlling methods of HIV was analyzed and discussed.

关 键 词：艾滋病病毒 动力学模型 基本的再生数量 整体稳定性 

分 类 号：O175.1[理学—数学]