Accounting for multi-delay effects in an HIV-1 infection model with saturated infection rate, recovery and proliferation of host cells

Biological models inherently contain delay. Mathematical analysis of a delay-induced model is, however, more difficult compare to its non-delayed counterpart. Difficulties multiply if the model contains multiple delays. In this paper, we analyze a realistic HIV-1 infection model in the presence and absence of multiple delays. We consider self-proliferation of CD4+T cells, nonlinear saturated infection rate and recovery of infected cells due to incomplete reverse transcription in a basic HIV-1 in-host model and incorporate multiple delays to account for successful viral entry and subsequent virus reproduction from the infected cell. Both of delayed and non-delayed system becomes disease-free if the basic reproduction number is less than unity. In the absence of delays, the infected equilibrium is shown to be locally asymptotically stable under some parametric space and unstable otherwise. The system may show unstable oscillatory behaviour in the presence of either delay even when the non-delayed system is stable. The second delay further enhances the instability of the endemic equilibrium which is otherwise stable in the presence of a single delay. Numerical results are shown to be in agreement with the analytical results and reflect quite realistic dynamics observed in HIV-1 infected individuals.