ABSTRACT

In this paper, we propose and analyse a delayed HIV-1 model with both viral and cellular transmissions and virus waning. We obtain the threshold dynamics of the proposed model, characterized by the basic reproduction number $R_0$. If $R_0<1$, the infection-free steady state is globally asymptotically stable; whereas if $R_0>1$, the system is uniformly persistent. When the delays are positive, we show that the intracellular delays in both viral and cellular infections may lead to stability switches of the infected steady state. Both analytical and numerical results indicate that if the effect of cell-to-cell transmission is ignored, then the risk of HIV-1 infection will be underestimated. Moreover, the viral load of model without virus waning is higher than the one of model with virus waning. These results highlight the important role of two ways of viral transmission and virus waning on HIV-1 infection.

摘要

在本文中，我们提出并分析了具有病毒和细胞传播以及病毒减弱的延迟 HIV-1 模型。我们获得了所提出模型的阈值动态，以基本再生数为特征${\mathrm{电阻}}_0$. 如果${\mathrm{电阻}}_0<1$，无感染稳态是全局渐近稳定的；而如果${\mathrm{电阻}}_0>1$，系统是一致持久的。当延迟为正时，我们表明病毒和细胞感染的细胞内延迟可能导致感染稳态的稳定性转换。分析和数值结果都表明，如果忽略细胞间传播的影响，那么 HIV-1 感染的风险将被低估。而且，没有病毒减弱的模型的病毒载量高于病毒减弱的模型。这些结果突出了病毒传播和病毒减弱两种方式对 HIV-1 感染的重要作用。