具有时滞和非线性感染率的HIV模型的稳定性和持续性  

Stability and Persistence for an HIV-1 Infection Model with Time Delay and Nonlinear Infection Rate

作　　者：韩溢[1] 杨志春[1] 

机构地区：[1]重庆师范大学数学学院,重庆400047

出　　处：《西南大学学报（自然科学版）》2013年第3期84-90,共7页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10971240);重庆市自然科学基金资助项目(CSTC2011BB0117;CSTC2012JJA40052);重庆市教委科研项目(KJ120630;KJ110628;KJ120615);教育部科技研究重点项目(212138)

摘　　要：研究了一类具有时滞和非线性感染率的HIV-1模型.借助于基本再生数和线性化模型的特征方程,获得了无病平衡点稳定性的阈值条件,并给出了无时滞和有时滞HIV模型间的地方病平衡点稳定性的蕴含关系.在此基础上,利用持续性理论得到了系统一致持续生存的充要条件.An HIV-1 model with intracellular delay and nonlinear infection rate is investigated in this stud- y. By the basic reproduction numbers and the characteristic equations of the linearized model,the threshold conditions for the stability of the disease-free equilibrium are obtained, and the contain relations for the stability of the endemic equilibrium of the HIV models with and without time delay are given. Based on that, some sufficient and necessary conditions ensuring the uniform persistence of the model are obtained by using the persistence theory.

关 键 词：HIV传染病模型 时滞 稳定性 持续性 

分 类 号：O175.1[理学—数学]