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

Wang, Jinliang ; Tian, Xinxin

Electronic journal of differential equations, Tome 2013 (2013)

Résumé

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.

Détail

Classification : 34K20, 92D25
Keywords: HBV infection model, delay, ctls, global stability