Dynamics of a within-host HIV/SARS-CoV-2 co-infection model with two intracellular delays

Abstract

This paper presents a delayed within-host model to investigate the intricate dynamics of HIV/SARS-CoV-2 co-infection. The analysis establishes the existence of unique positive and bounded solutions under specified initial conditions. The healthy, the single HIV infection, the single SARS-CoV-2 infection and the HIV/SARS-CoV-2 co-infection steady states, are computed contingent upon threshold parameters $R_H$, $R_C$, and $R_{HC}$. Through rigorous examination of characteristic equations, the local stability of pivotal steady states-namely, the healthy state and the HIV/SARS-CoV-2 co-infection state is elucidated, alongside the identification of Hopf bifurcations using delays as bifurcation parameters. Intriguingly, theoretical analyses reveal that delays exert no discernible influence on the stability of the healthy state, whereas they may destabilize the HIV/SARS-CoV-2 co-infection state under specific conditions. Moreover, employing appropriate Lyapunov functions confirms the global asymptotic stability of all steady states. Complementary numerical simulations are conducted to augment theoretical insights and delineate the nuanced impact of each time delay, albeit without explicit Hopf bifurcation simulations.