A NUMERICAL METHOD FOR A DIFFUSIVE HBV INFECTION MODEL WITH MULTI-DELAYS AND TWO MODES OF TRANSMISSION

In this study, we propose a numerical method for four partial differential equations that describe the dynamics of hepatitis B virus (HBV) with capsids, three discrete delays and two modes of transmission which are the classical virus-to-cell infection and the direct cell-to-cell transmission. Firstly, we show that the proposed numerical method maintains the positivity and boundedness of solutions in order to ensure the well-posedness of the problem. By constructing Lyapunov functionals, we prove that the numerical method preserves the global dynamical behaviors of the corresponding continuous system for any spacial and temporal step sizes. The delayed discrete model obtained by the proposed numerical method includes various special cases available in the literature. To depict the theoretical results graphically, we present some numerical illustrations at the end of the study.