摘要
建立了一类较广泛的HIV感染CD4+T细胞病毒动力学模型,给出了一个感染细胞在其整个感染期内产生的病毒的平均数(基本再生数)R0的表达式,运用Lyapunov原理和Routh-Hurwitz判据得到了该模型的未感染平衡点与感染平衡点的存在性与稳定性条件.同时也得到了模型存在轨道渐近稳定周期解和系统持续生存的条件,并通过数值模拟验证了所得到的结果.
This paper formulates a class of generalized viral dynamical model for HIV infection of CD4+T cells.The explicit expression of the basic reproduction number R0(it represents the average number of secondary infections caused by a single primary actively infected T cell introduced into a pool of susceptible T cells during its entire infection period) is obtained.The conditions for the existence and stability of the uninfected and infected equilibria are given.The existence conditions of an orbitally asymptotically stable periodic solution are also obtained by using Lyapunov function,additive compound matrix theory and three-dimensional competitive system theory.The theoretical results obtained in this paper are supported by numerical simulation.
作者
邵莉
李学志
SHAO Li;LI Xue-zhi(Department of Mathematics and Computer Science,Xinyang Vocational and Technical College,Xinyang 464000,China;College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China)
出处
《数学的实践与认识》
2021年第6期120-130,共11页
Mathematics in Practice and Theory
关键词
HIV病毒动力学模型
感染平衡点
全局稳定
一致持续
周期解
HIV viral dynamical model
infected equilibrium
global stability
uniform persistence
periodic solution
