具有潜伏期和免疫应答的HIV感染模型的全局稳定性
发布时间：2018-11-28 18:29
【摘要】：本文考虑具有CTL免疫应答和细胞内部潜伏阶段的HIV感染数学模型,得到其基本再生数,通过构造适用的Lyapunov函数,研究该模型的健康平衡点和感染平衡点的稳定性.当基本再生数不大于1时,健康平衡点在可行域上是全局稳定的,即HIV在个体体内最终灭绝;当基本再生数大于1时,模型存在惟一的感染平衡点在可行域上是全局稳定的,即HIV在个体体内呈现持续存在状态,且其浓度最终趋于一个常数.
[Abstract]:In this paper, we consider the mathematical model of HIV infection with CTL immune response and latent phase in cells, and obtain its basic regeneration number. By constructing the suitable Lyapunov function, we study the stability of the healthy equilibrium point and the infection equilibrium point of the model. When the number of basic regeneration is less than 1, the health equilibrium is globally stable in the feasible region, that is, the HIV is extinct in the individual body. When the basic regeneration number is greater than 1, the unique infection equilibrium point of the model is globally stable in the feasible region, that is, the HIV is persistent in the individual body and its concentration tends to be a constant.
【作者单位】： 空军工程大学理学院;
【基金】：国家自然科学基金(11371369)
【分类号】：O175
[Abstract]:In this paper, we consider the mathematical model of HIV infection with CTL immune response and latent phase in cells, and obtain its basic regeneration number. By constructing the suitable Lyapunov function, we study the stability of the healthy equilibrium point and the infection equilibrium point of the model. When the number of basic regeneration is less than 1, the health equilibrium is globally stable in the feasible region, that is, the HIV is extinct in the individual body. When the basic regeneration number is greater than 1, the unique infection equilibrium point of the model is globally stable in the feasible region, that is, the HIV is persistent in the individual body and its concentration tends to be a constant.
【作者单位】： 空军工程大学理学院;
【基金】：国家自然科学基金(11371369)
【分类号】：O175
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