基于Logistic增长、药物治疗和潜伏感染的HIV模型研究.pdfVIP

Advances in Applied Mathematics 应用数学进展, 2016, 5(4), 577-590 Published Online November 2016 in Hans. /journal/aam /10.12677/aam.2016.54067 Study on the HIV Model Based on Logistic Growth, Drug Treatment and Latent Infection Man Zhou, Xin Che, Xuemeng Fan, Linwei Xiao, Yan Wang Science Department, China University of Petroleum (East China), Qingdao Shandong th th th Received: Oct. 19 , 2016; accepted: Nov. 7 , 2016; published: Nov. 11 , 2016 Copyright © 2016 by authors and Hans Publishers Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). /licenses/by/4.0/ Open Access Abstract According to HIV infection process in infected individuals, this paper establishes HIV dynamics model of logistic growth, drug treatment and latent infection, to simulate the relationship among virus particles, T cells and drug treatment in the infection process. Then the stability theory of differential equations is used to analyze and discuss the global dynamics of the model. Finally by the way of comparatively analyzing different models, we get a more realistic process of HIV infec- tion, which is benefit to research the mechanism of HIV infection. Keywords HIV Virus, Latent Infection, Drug Treatment, Logistic Growth 基于Logistic增长、药物治疗和潜伏感染的HIV 模型研究 周 漫，车 欣，范雪萌，肖林伟，王 艳 中国石油大学(华东)理学院，山东 青岛 收稿日期：2016年10月19 日；录用日期：2016年11月7 日；发布日期：2016年11月11 日 文章引用: 周漫, 车欣, 范雪萌, 肖林伟, 王艳. 基于Logistic 增长、药物治疗和潜伏感染的HIV 模型研究[J]. 应用数学 进展, 2016, 5(4): 577-590. /10.12677/aam.2016.54067 周漫 等 摘 要 本文根据HIV在感染者体内的感染过程，建立具有Logistic增长、药物治疗和潜伏感染的HIV动力学模型 来模拟感染过程中病毒颗粒、T细胞和药物治疗之间的相互关系；然后运用微分方程的稳定性理论，对