Global dynamics of a cytokine-enhanced viral infection model with distributed delays and optimal control analysis

This paper analyzed a cytokine-enhanced viral infection model incorporating three distributed delays: $(1)$ Intracellular delays in infected ${\mathrm{C}\mathrm{D}4}^{+}$ T cells induced by inflammatory cytokines and viruses, $(2)$ delays in ${\mathrm{C}\mathrm{D}4}^{+}$ T cell activation at inflammatory sites and subsequent cytokine production, and $(3)$ viral replication delays. By using Lyapunov functionals and LaSalle's invariance principle, we established that each equilibrium exhibits global asymptotic stability under certain conditions. Furthermore, we formulated an optimality system that incorporates delays and then characterized it using Pontryagin's Maximum Principle. Numerical simulations have confirmed the global asymptotic stability of all equilibrium points in the system. Furthermore, for the optimal control system, our simulations not only justified the necessity of incorporating time delay in modeling inflammatory cytokine production but also highlighted the critical importance of tailoring precise HIV treatment strategies according to specific time-delay values.