一类HIV传播人群的非线性动力学模型  

A Class of Nonlinear Dynamic Model of Human Groups for HIV Transmission

作　　者：冯依虎 汪维刚 莫嘉琪 FENG Yihu;WANG Weigang;MO Jiaqi(Department of Electronics and Information Engineering,Bozhou University,Bozhou 236800,Anhui Province,China;Hefei Preschool Education College,Hefei 230011,China;School of Mathematics ＆ Statistics,Anhui Normal University,Wuhu 241003,Anhui Province,China)

机构地区：[1]亳州学院电子与信息工程系,安徽亳州236800 [2]合肥幼儿师范高等专科学校,合肥230011 [3]安徽师范大学数学与统计学院,安徽芜湖241003

出　　处：《吉林大学学报（理学版）》2018年第4期779-785,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:41275062);安徽省教育厅自然科学重点基金(批准号:KJ2015A347;KJ2017A901;KJ2017A702);安徽省高校优秀青年人才支持计划重点项目(批准号:gxyqZD2016520);安徽省教育科学规划项目(批准号:JG10068);亳州学院重点教学研究项目(批准号:2017zdjy02);亳州学院自然科学研究重点项目(批准号:BYZ2017B02)

摘　　要：考虑人体免疫缺陷病毒(HIV)传播的动力学模型,利用流行性传染病区域的人群传播规律,提出一类HIV传播的动力学系统.先利用泛函同伦映射方法,得到一类HIV传播动力学非线性系统近似解的序列及其一致收敛性,并举例得到各次近似解,再对HIV传播动力学系统的解进行定量和定性分析.结果表明,利用近似解的表示式可调节感染者人数和易感者人数的分布.We considered a class of dynamic model of human immunodeficiency virus（HIV）transmission and proposed a class of HIV transmission dynamic system by using the rule of population transmission in epidemic contagion region.Firstly,using the functional homotopic mapping method,we obtained the sequence of approximate solutions of a class of HIV nonlinear transmission dynamic system and their uniformly convergence,and gave an example to get all the approximate solutions.Then the quantitative and qualitative analysis of the solution for HIV transmission dynamic system was carried out.The results show that the expressions of approximate solution can regulate the distribution for the number of infected persons and susceptible persons.

关 键 词：HIV传播人群 非线性动力学模型 同伦映射 近似解 

分 类 号：O175.14[理学—数学]