Dynamics Analysis of a Delayed HIV Model With Latent Reservoir and Both Viral and Cellular Infections

Abstract

This paper presents an HIV model with latent reservoir and a constant production rate of cytotoxic T lymphocytes (CTLs). The system incorporates two delays, intracellular delay ${\tau }_1$ and immune response delay ${\tau }_2$, and considers two mechanisms of viral transmission in vivo: cell-to-cell and virus-to-cell. Based on the initial condition, a key threshold in the model, namely, the basic reproduction number $R_0$ is obtained. Our focus is to investigate the impact of saturated immune delay on viral infection when CTLs are introduced at a constant rate. By constructing Lyapunov functionals, the stability conditions of equilibrium $E_0$ and equilibrium $E^{\ast }({\tau }_2=0)$ are established. Theoretical analysis indicates that equilibrium $E^{\ast }$ no longer remains stable and generates a Hopf bifurcation as immune delay ${\tau }_2$ changes. Numerical simulations are conducted to validate the main theoretical results, and sensitivity analysis is used to evaluate the impact of the parameters on the threshold. Through these simulations, the general patterns of dynamic behavior of the model are revealed. In particular, when ${\tau }_1>0$ and ${\tau }_2>0$, the dynamics of the endemic equilibrium $E^{\ast }$ exhibit complex behavior.