A Mathematical Model of Within-Host HBV and HTLV-1 Co-Infection Dynamics

Hepatitis B virus (HBV) and human T-lymphotropic virus type 1 (HTLV-1) are blood-borne pathogens with overlapping transmission routes, resulting in an increased prevalence of HBV among individuals infected with HTLV-1. Notwithstanding the widespread application of mathematical modeling to the study of each virus in isolation, the within-host dynamics of HBV–HTLV-1 co-infection remain insufficiently characterized. This study introduces a novel within-host co-infection model that characterizes the interactions between HBV and HTLV-1, where HTLV-1 infects CD4+ T cells and HBV targets hepatocytes. A comprehensive qualitative analysis yields four threshold parameters (Ri,i=1,2,3,4) governing the existence and stability of equilibrium points, with global stability established using Lyapunov functions. Numerical simulations validate the analytical results, and sensitivity analysis identifies parameters that most strongly influence the basic reproduction numbers for HBV (R1) and HTLV-1 (R2) mono-infections. Our results corroborate that, in patients with HBV, the presence of HTLV-1 contributes to an elevated HBV viral load and CD4+ T cells play a crucial role in controlling HBV infection.