具有逃逸阶段的HIV模型的稳定性研究

Study on the Stability of HIV Model with Escape Stage

摘要: HIV病毒动力学的数学模型用于描述病毒和寄主细胞之间是相互作用，研究人类免疫缺陷病毒(HIV)病毒动态变化的数学模型。这个模型的一个主要特征是，包含一个感染单元的逃逸阶段，代表感染的T细胞尚未开始产生新病毒的阶段，利用分数阶微分方程稳定性理论，建立一个由四个非线性常微分方程组成的模型。首先，考虑模型只有在非负解和正解存在的情况下才有意义，讨论分数阶常微分方程正解的存在性问题。其次，将分数阶引入HIV感染CD4⁺ T细胞的模型，通过分析，得到方程的正解的存在性和平衡点渐近稳定性条件。最后借助MATLAB进行数值模拟，提供了一个更加完整的系统动力学，同时也验证模型结果是否正确。

Abstract: A mathematical model of HIV dynamics is used to describe the interaction between the virus and the host cell, study the mathematical model of dynamic change of human immunodeficiency virus (HIV) virus. One of the main features of this model is that it contains an escape phase of the infection unit, a phase in which infected T cells have not yet begun to produce new viruses, using the fractional differential equation stability theory, build a model of four Linear differential equation. First, we consider that the model is meaningful only if non-negative solutions and positive solutions exist, and discuss the existence of fractional ordinary differential equation positive solutions. Secondly, the fractional order is introduced into the model of HIV infected CD4⁺ T cells. Through analysis, the existence of positive solution and the asymptotic stability of equilibrium point are obtained. Finally, MATLAB is used to carry out numerical simulation to provide a more complete System dynamics, and also verify the correctness of the model results.