Analysis of delayed HIV-1 dynamics model with inflamma-tory cytokines and cellular infection

The purpose of this research is to develop a mathematical model to study the dynamics of human immunodeficiency virus type -1 (HIV -1) infection with inflammatory cytokines. The model incorporates two modes of infection (viral and cellular), two immune responses (antibody and cytotoxic T lymphocyte (CTL)) and two types of distributed -time delays. We demonstrate that the model's solutions are non -negative and eventually bounded, demonstrating the suggested model's biological viability. We find the equilibrium points of the model and get the sufficient conditions for their existence and stability.The Lyapunov approach is utilized to investigate the global stability of the equilibria. We determine which parameters most affect the basic reproduction number using sensitivity analysis. We reformulate our model by including the influence of three classes of antiretroviral drug therapies. We determine a critical efficacy for each antiretroviral therapy, after which HIV -1 will be eradicated entirely if treatment effectiveness surpasses this threshold. We also establish that the estimated treatment efficacy will be lower than what is necessary to eliminate the virus entirely if the inflammatory cytokines and/or cellular infection are ignored. Moreover, we show that time delay has an identical effect on virus elimination as antiretroviral therapy. It is also shown that, prolonging time delays can successfully reduce the basic reproduction number and stop HIV -1 replication. According to our findings, time delay, cellular infection, and inflammatory cytokines are crucial components of the HIV -1 model and should not be disregarded. The study's analytical and numerical findings advance our knowledge of HIV -1 dynamics and may help develop more effective HIV -1 management plans.