一个带有ATL过程的HTL V-I感染的时滞模型

One Discrete Time Delay Model of HTL V-I Infection and ATL Progression

本文提出并分析了两个关于人体T-细胞淋巴回归Ⅰ型病毒(HTL V-I)感染并带有坏死白血病细胞(ATL)进程的数学模型,一个常微分方程模型,一个离散时滞模型.首先对常微分方程模型进行了分析,运用相应的特征方程得到一个阈值Ro(CD4^+ T-细胞的基本再生数).当R_0≤1时,仅有未染病平衡态存在,并且给出了其稳定性;当R_0>1时,有一个染病稳定态存在,并且此时它是稳定的.然后,我们在常微分方程模型中引入了一个离散时滞,通过对时滞模型的超越特征方程的分析,导出了与常微分方程模型中同样的稳定性条件,即时滞模型平衡态的稳定性与时滞的具体值无关.

In this paper,we propose and discuss two mathematical models of HTL V-I infection and ATL progression,one ODE model and one discrete time delay model.First,by analyzing the characteristic equation of the ODE model,it is shown that the dynamics of the ODE model is determined by the threshold of the parameters,that is,the basic reproductive number （of CD4~＋ T-cell ） R_0.If the threshold value is less than one,i.e.R_01,only the disease-free equilibrium exist and it is stable.While the threshold value is greater than one,i.e.R_01,there is a unique endemic equilibrium,and it is stable.Then,we introduce one discrete time delay in the ODE model.By analyzing the transcendental characteristic equation of the delay model,we analytically derived stability conditions for the infected equilibrium in terms of the parameters and independent of the delay,i.e.identical to the ODE model.