一类具有饱和感染率与治愈率的HIV病理模型
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引用本文:刘祥东, 刘 澄.一类具有饱和感染率与治愈率的HIV病理模型[J].经济数学,2011,(3):1-5
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刘祥东, 刘 澄 (北京科技大学 东陵经济管理学院, 北京 100083) 
中文摘要:将治愈率以及饱和感染率引入基本的HIV病理模型, 构建一个改进的HIV病理模型. 利用微分动力系统的相关理论, 证明改进模型中无病平衡点和染病平衡点的全局渐近稳定性, 然后执行相关的数值模拟以验证所得结论. 研究结果表明: 在饱和感染率的条件下, HIV感染进程变缓; 同时提高治愈率能有效地控制HIV感染.
中文关键词:全局稳定性  HIV感染  治愈率  饱和感染率
 
An HIV Pathogenesis Model with Saturated Infection Rate and Cure rate
Abstract:After introducing the cure rate and the saturated infection rate into the basic HIV pathogenesis model, this paper constructsed an improved HIV pathogenesis model. It proves the globally asymptotical stability of both the uninfected equilibrium point and the infected steady state by applying the related theory of differential dynamical systems, and then numerical simulations were carried out to check the main results. The investigation results indicate that HIV infection process will become slow under the condition of saturated infection rate, and that improving cure rate is able to control HIV infection efficiently.
keywords:global stability  HIV infection  cure rate  saturated infection rate
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