Abstract

This study presents two mathematical models to improve understanding of cytokine-mediated effects on abortive HIV-1 infection. The models describe interactions among healthy CD4+ T cells, abortively and actively HIV-1-infected CD4+ T cells, in- flammatory cytokines, and free HIV-1 particles. In the second model, four types of dis- tributed time delays are incorporated. The biological feasibility of the models is established by demonstrating the non-negativity and boundedness of solutions. Two equilibrium points are identified, and their existence and stability are characterized in terms of the basic repro- duction number ℜ0. The global stability of the equilibria is analyzed using the Lyapunov method. Numerical simulations support the analytical results. Sensitivity analysis is con- ducted to identify key parameters influencing ℜ0. The impact of time delays on HIV-1 progression is also examined. The findings suggest that longer delays can significantly reduce ℜ0, potentially suppressing HIV-1 replication.