一类具有免疫反应和抗逆转录病毒治疗的HIV病毒传染病模型的动力学性态分析

发布时间：2018-03-09 13:33

本文选题：传染病模型　切入点：CTL细胞　出处：《中北大学学报(自然科学版)》2017年03期 　论文类型：期刊论文

【摘要】：研究了一类具有免疫反应和抗逆转录病毒治疗的HIV病毒传染病模型的动力学性态.通过理论分析,给出疾病发生的基本再生数R_0:当R_01时,系统只存在无病平衡点,且是局部渐近稳定的;当R_01时,系统存在惟一的正平衡点,且是局部渐近稳定的.通过数值模拟发现,当R_01时,无病平衡点是全局渐近稳定的,即疾病消失;当R_01时,正平衡点是全局渐近稳定的,即疾病流行.通过分析发现CTL细胞免疫反应的有效率越高,CD4~+T细胞被再次感染的概率越低,即HIV患者的免疫力提高,有效地控制了疾病的传播.
[Abstract]:The dynamic behavior of a class of HIV viral infectious disease models with immune response and antiretrovirals therapy was studied. By theoretical analysis, the number of basic regenerations of the disease was given: when R01, there were only disease-free equilibrium points in the system. And it is locally asymptotically stable; when R _ S _ 1 exists, the system has a unique positive equilibrium and is locally asymptotically stable. It is found by numerical simulation that the disease-free equilibrium is globally asymptotically stable when R _ s _ (01) is stable, that is, the disease disappears when R _ _ (01). The positive equilibrium is globally asymptotically stable, that is, disease prevalence. It is found that the higher the effective rate of immune response of CTL cells, the lower the probability of reinfection of CD4T cells, that is, the immunity of patients with HIV is improved, and the spread of disease is effectively controlled.
【作者单位】：中北大学理学院;
【基金】：国家自然科学基金资助项目(11201434) 山西省回国留学人员科研资助项目(2013-087) 山西省留学回国人员科技活动择优资助项目
【分类号】：O175

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