Stability analysis for viral infection model with multitarget cells, Beddington-DeAngelis functional response, and humoral immunity (Q1723450)

Summary: We formulate a \((2n+2)\)-dimensional viral infection model with humoral immunity, \(n\) classes of uninfected target cells and \(n\) classes of infected cells. The incidence rate of infection is given by nonlinear incidence rate, Beddington-DeAngelis functional response. The model admits discrete time delays describing the time needed for infection of uninfected target cells and virus replication. By constructing suitable Lyapunov functionals, we establish that the global dynamics are determined by two sharp threshold parameters: \(\mathfrak{R}_0\) and \(\mathfrak{R}_1\). Namely, a typical two-threshold scenario is shown. If \(\mathfrak{R}_0 \leq 1\), the infection-free equilibrium \(P_0\) is globally asymptotically stable, and the viruses are cleared. If \(\mathfrak{R}_1 \leq 1 < \mathfrak{R}_0\), the immune-free equilibrium \(P_1\) is globally asymptotically stable, and the infection becomes chronic but with no persistent antibody immune response. If \(\mathfrak{R}_1 > 1\), the endemic equilibrium \(P_2\) is globally asymptotically stable, and the infection is chronic with persistent antibody immune response.