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, inflammatory cytokines, and free HIV-1 particles. In the second model, four types of distributed 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 reproduction number ℜ0. The global stability of the equilibria is analyzed using the Lyapunov method. Numerical simulations support the analytical results. Sensitivity analysis is conducted 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.