具有体液免疫和细胞免疫的反应扩散HIV病毒模型

Reactive Diffusion HIV Virus Model with Humoral and Cellular Immunity

本文基于HIV病毒在人体内的动态变化过程和人体的两类免疫机制,提出了一种具有体液免疫和细胞免疫的反应扩散HIV病毒模型.利用比较原理和极值原理证明了该模型非负解的存在性及有界性.通过定义不同患病阶段下两个关键阈值,并利用李亚普诺夫理论分析了无病平衡点和两类患病平衡点的全局动力学行为.最后,利用数值实例子验证了理论结果正确性.

In this paper,based on the dynamic process of HIV virus and two types of immune mechanisms in human body,a reactive diffusion HIV virus model with humoral and cellular immunity is proposed.The existence and boundedness of the non-negative solution of the model are proved by using the comparison principle and the extreme value principle.By defining two critical thresholds under different disease stages and using Lyapunov’s theory,the dynamic behaviors of the disease-free equilibrium point and the two types of diseased equilibrium points are analyzed.Finally,the correctness of the theoretical results is verified by using numerical real examples.