A within-host virus model with multiple infected stages under time-varying environments

•We propose a within-host virus model with multiple infected stages under time-varying environments.•We establish the sufficient conditions for both persistent HIV infection and clearance of HIV infection.•We extend the results for the related within-host model with single infected stage.•We generalize the works for corresponding autonomous within-host system with multiple infected stages.

HIV-1 infection and treatment may occur in the non-constant environment due to the time-varying drug susceptibility and growth of target cells. In this paper, we propose a within-host virus model with multiple stages for infected cells under time-varying environments, to study how the multiple infected stages affect on the counts of viral load and CD4++-T cells. We establish the sufficient conditions for both persistent HIV infection and clearance of HIV infection based on two positive constants R*, R*. When the system is under persistent infection, we further obtained detailed estimates of both the lower and upper bounds of the viral load and the counts of CD4++-T cells. Furthermore, numerical simulations are carried out to verify our analytical results and demonstrate the combined effects of multiple infected stages and non-constant environments, and reflect that both persistence and clearance of infection are possible when R* < 1 < R* holds. In particular, the numerical results exhibit the viral load of system with multiple infected stages may be less than that with single infected stage, and simulate the effect of time-varying environment of the autonomous system with multiple infected stages. We expect that our theoretical and simulation results can provide guidance for clinical therapy for HIV infections.