带有年龄结构和抗药物治疗的HIV模型
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摘要
HIV/AIDS个体的传染力受感染年龄的影响,抗药物治疗可有效控制其传播.根据这些特点,建立了带有感染年龄和抗药物治疗的HIV模型,分析了系统解的存在性,利用Lyapunov函数研究了系统稳态解的稳定性.
The infect individuals of HIV/AIDS is affected by the age of infection,antiretroviral therapy can effectively control its spread. According to these characteristics,an age-infection-structured HIV model with antiretroviral therapy is established,the existence of the system solution is analyzed. Further,the stability of the system stable solution is studied using the Lyapunov function.
The infect individuals of HIV/AIDS is affected by the age of infection,antiretroviral therapy can effectively control its spread. According to these characteristics,an age-infection-structured HIV model with antiretroviral therapy is established,the existence of the system solution is analyzed. Further,the stability of the system stable solution is studied using the Lyapunov function.
引文
[1]NELSON P W,GILCHRIST M A,COOMBS D,et al. An age-structured model of HIV infection that allows for variations in the production rate of viral particles and the death rate of productively infected cells[J]. Mathematical Biosciences and Engineering,2017,1(2):267-288.
[2]HUANG G,LIU X N,TAKEUCHI Y. Lyapunov functions and global stability for age-structured HIV infection model[J].SIAM Journal on Applied Mathematics,2012,72(1):25-38.
[3]RONG Libin,FENG Zhilan,PERELSON A S. Mathematical analysis of age-structured HIV-1 dynamics with combination antiretroviral therapy[J]. SIAM Journal on Applied Mathematics,2007,67(3):731-756.
[4]王俊芳.传染病模型的稳定性分析[D].太原:中北大学,2008.WANG Junfang. Stability analysis of infectious disease model[D]. Taiyuan:Zhongbei University,2008.
[5]唐琪,卢洪洲.艾滋病流行现状及防治策略探讨[J].复旦学报(医学版),2017,44(6):744-751.TANG Qi,LU Hongzhou.AIDS epidemic status and prevention and control strategies[J].Fudan University Journal of Medical Sciences,2017,44(6):744-751.
[6]张兴权.长效抗逆转录病毒药物研究进展[J].中国病毒病杂志,2018,8(1):6-10.ZHANG Xingquan. Research progress of long-acting antiretroviral drugs[J]. Chinese Journal of Viral Diseases,2018,8(1):6-10.
[7]ANELONE A J N,SPURGEON S K. Prediction of the containment of HIV infection by antiretroviral therapy-avariable structure control approach[J]. IET Systems Biology,2017,11(1):44-53.
[8]柳合龙,佟宁,靳彦培.带有年龄结构和治疗策略的连续和脉冲HIV/AIDS模型[J].信阳师范学院学报(自然科学版),2017,30(4):517-520,657.LIU Helong,TONG Ning,JIN Yanpei. Studies on two class-age-structured HIV/AIDS models with continuous and impulsive drug-treatment strategies[J]. Journal of Xinyang Normal University(Natural Science Edition),2017,30(4):517-520,657.
[9]MARTCHEVA Maia,LI Xuezhi. Competitive exclusion in an infection-age structured model with environmental transmission[J]. Journal of Mathematical Analysis and Applications,2013,408(1):225-246.
[10]柳合龙,张娅莉,程传敏.一类受媒体影响的随机HIV模型[J].信阳师范学院学报(自然科学版),2016,29(2):157-160.LIU Helong,ZHANG Yali,CHENG Chuanmin. A class of stochastic model of HIV affected by the media[J]. Journal of Xinyang Normal University(Natural Science Edition),2016,29(2):157-160.
[11]MAGAL P,MCCLUSKEY C C,WEBB G F. Lyapunov functional and global asymptotic stability for an infection-age model[J]. Applicable Analysis,2010,9(7):1109-1140.
[2]HUANG G,LIU X N,TAKEUCHI Y. Lyapunov functions and global stability for age-structured HIV infection model[J].SIAM Journal on Applied Mathematics,2012,72(1):25-38.
[3]RONG Libin,FENG Zhilan,PERELSON A S. Mathematical analysis of age-structured HIV-1 dynamics with combination antiretroviral therapy[J]. SIAM Journal on Applied Mathematics,2007,67(3):731-756.
[4]王俊芳.传染病模型的稳定性分析[D].太原:中北大学,2008.WANG Junfang. Stability analysis of infectious disease model[D]. Taiyuan:Zhongbei University,2008.
[5]唐琪,卢洪洲.艾滋病流行现状及防治策略探讨[J].复旦学报(医学版),2017,44(6):744-751.TANG Qi,LU Hongzhou.AIDS epidemic status and prevention and control strategies[J].Fudan University Journal of Medical Sciences,2017,44(6):744-751.
[6]张兴权.长效抗逆转录病毒药物研究进展[J].中国病毒病杂志,2018,8(1):6-10.ZHANG Xingquan. Research progress of long-acting antiretroviral drugs[J]. Chinese Journal of Viral Diseases,2018,8(1):6-10.
[7]ANELONE A J N,SPURGEON S K. Prediction of the containment of HIV infection by antiretroviral therapy-avariable structure control approach[J]. IET Systems Biology,2017,11(1):44-53.
[8]柳合龙,佟宁,靳彦培.带有年龄结构和治疗策略的连续和脉冲HIV/AIDS模型[J].信阳师范学院学报(自然科学版),2017,30(4):517-520,657.LIU Helong,TONG Ning,JIN Yanpei. Studies on two class-age-structured HIV/AIDS models with continuous and impulsive drug-treatment strategies[J]. Journal of Xinyang Normal University(Natural Science Edition),2017,30(4):517-520,657.
[9]MARTCHEVA Maia,LI Xuezhi. Competitive exclusion in an infection-age structured model with environmental transmission[J]. Journal of Mathematical Analysis and Applications,2013,408(1):225-246.
[10]柳合龙,张娅莉,程传敏.一类受媒体影响的随机HIV模型[J].信阳师范学院学报(自然科学版),2016,29(2):157-160.LIU Helong,ZHANG Yali,CHENG Chuanmin. A class of stochastic model of HIV affected by the media[J]. Journal of Xinyang Normal University(Natural Science Edition),2016,29(2):157-160.
[11]MAGAL P,MCCLUSKEY C C,WEBB G F. Lyapunov functional and global asymptotic stability for an infection-age model[J]. Applicable Analysis,2010,9(7):1109-1140.