Electron. J. Diff. Equ., Vol. 2013 (2013), No. 94, pp. 1-11.

Global stability of a delay differential equation of hepatitis B virus infection with immune response

Jinliang Wang, Xinxin Tian

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.

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Jinliang Wang
School of Mathematical Science, Heilongjiang University
Harbin 150080, China
email: jinliangwang@yahoo.cn
Xinxin Tian
School of Mathematical Science, Heilongjiang University
Harbin 150080, China
email: xinxintian@yahoo.cn

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