A delayed HIV-1 model with cell-to-cell spread and virus waning

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 $$ . If $$ , the infection-free steady state is globally asymptotically stable; whereas if $$ , 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.