Global stability of in-host viral models with humoral immunity and intracellular delays

In this paper, we investigate the dynamical behavior of in-host viral models with humoral immunity and intracellular delays. For both models, using the method of Lyapunov functional, we establish that the global dynamics are determined by two threshold parameters R0 and R1. If R0 ⩽ 1, the uninfected equilibrium E0 is globally asymptotically stable, and the viruses are cleared. If R1 ⩽ 1 < R0, the infected equilibrium without B cells response E1∗ is globally asymptotically stable, and the infection becomes chronic but with no persistent B cells response. If R1 > 1, the infected equilibrium with B cells response E2∗ is globally asymptotically stable, and the infection is chronic with persistent B cells response. Alone with some numerical simulations.