| Abstract: |
| In view of the molecular biological mechanism of the cytotoxic T lymphocytes proliferation induced by Hepatitis B virus infection in vivo, a novel dynamical model with delay interval is proposed. The delay interval is determined by delay center and delay radius. We derive the basic reproduction number $R_0$ for the viral infection and obtain that the virus-free equilibrium (VFE) is globally asymptotically stable if $R_0 < 1$. When $R_0 > 1$, besides VFE, the unique virus-survived equilibrium (VSE) exists, and the conditions of its asymptotical stabilization are obtained. Moreover, we study the Hopf bifurcations induced by the two delay parameters. The results indicate that both these two delay parameters can lead to periodic fluctuations at VSE, but only the smaller delay radius will destabilize the system, which is different from the classical discrete delay or distributed delay. Numerical simulations indicate that the proposed model can capture the profiles of the clinical data of two untreated chronic hepatitis B patients. The ability of delay interval to destabilize the system is between discrete delay and distributed delay, and the delay center plays the primary role. Pharmaceutical treatment can affect the stability of VSE and induce the fast-slow periodic phenomenon. |
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