Global Stability of a Delay Differential Equation of Hepatitis B Virus Infection with Immune Response

The global stability for a delayed HBV infection model with CTL immune response is investigated. We show that the global dynamics is determined by two sharp thresholds, basic reproduction number <0 and CTL immune-response reproduction number <1. When <0 ≤ 1, the infection-free equilibrium is globally asymptotically stable, which means that the viruses are cleared and immune is not active; when <1 ≤ 1 < <0, the CTL-inactivated infection equilibrium exists and is globally asymptotically stable, which means that CTLs immune response would not be activated and viral infection becomes chronic; and when <1 > 1, the CTL-activated infection equilibrium exists and is globally asymptotically stable, in this case the infection causes a persistent CTLs immune response. Our model is formulated by incorporating a Cytotoxic T lymphocytes (CTLs) immune response to recent work [Gourley, Kuang, Nagy, J. Bio. Dyn., 2(2008), 140-153] to model the role in antiviral by attacking virus infected cells. Our analysis provides a quantitative understandings of HBV replication dynamics in vivo and has implications for the optimal timing of drug treatment and immunotherapy in chronic HBV infection.