具有VCT意识及媒体报道影响的HIV/AIDS感染动力学模型  

A dynamic model of HIV/AIDS infection with VCT awareness and media coverage

作　　者：苑运强 罗颜涛 胡西尼格尔·吐尔地 Yuan yunqiang;Luo Yantao;Husinagar Turdi(College of Mathematics and Systems Science,Xinjiang University,Urumqi 830017,China)

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830017

出　　处：《河南师范大学学报（自然科学版）》2025年第1期43-49,共7页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(12201540);新疆维吾尔自治区自然科学基金(2022D01C64);新疆高校科研项目(XJEDU2021Y001).

摘　　要：构建一类具有VCT(voluntary counseling and testing)意识及媒体报道影响的HIV/AIDS感染动力学模型.首先得到模型解的适定性,并给出模型的基本再生数.其次,借助Hurwitz判别法及Lyapunov函数分析模型的阈值动力学,当R_(0)<1时无病平衡点局部渐近稳定且当R_(0)≤1时全局渐近稳定;当R_(0)>1时,地方病平衡点局部渐近稳定.进一步,结合持续生存理论给出疾病的一致持续性.最后,数值模拟表明随着VCT意识比例的提高,艾滋病患者人数的峰值逐渐降低,而随着信息失效率的增大,艾滋病患者人数的峰值将有所提高.This paper constructs a dynamic model of HIV/AIDS infection with VCT awareness and media coverage.Firstly,we obtain the well-posedness and the basic regeneration number of the model.Secondly,according to the Hurwitz discrimination and Lyapunov function,the threshold dynamics of the model were analyzed.When R_(0)<1,the disease-free equilibrium is locally asymptotically stable,and when R_(0)≤1,it is globally asymptotically stable.When R_(0)>1,the endemic equilibrium is locally asymptotically stable.Furthermore,the uniformly persistence of the disease is given according to continuous survival theory.Finally,the numerical simulation shows that with the increase of VCT awareness ratio,the peak number of AIDS patients will gradually decrease,and with the increase of information failure rate,the peak number of AIDS patients will be increased.

关 键 词：HIV动力学模型 VCT意识 媒体报道 稳定性 

分 类 号：O175.1[理学—数学]