Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 94, pp. 1-11.

Title: Global stability of a delay differential equation of hepatitis
       B virus infection with immune response
        
Authors: Jinliang Wang (Heilongjiang Univ., Harbin, China)
         Xinxin Tian   (Heilongjiang Univ., Harbin, China)

Abstract:
 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 $\Re_0$
 and CTL immune-response reproduction number $\Re_1$. When $\Re_0 \leq 1$,
 the infection-free equilibrium is globally asymptotically stable, which
 means that the viruses are cleared and immune is not active;
 when $\Re_1 \leq 1 < \Re_0$, 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 $\Re_1 > 1$, 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.

Submitted  March 4, 2013. Published April 11, 2013.
Math Subject Classifications: 34K20, 92D25.
Key Words: HBV infection model; delay; CTLs; global stability.