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In this paper, we modify the HBV model proposed in [1] to include the spatial variations of free antibody, virus-antibody complexes, and free virus. By using comparison arguments and theory of uniform persistence, we can show that the persistene/extinction of HBV can be determined by the reproduction number(s).Markovian model is widely used to study cardiac electrophysiology and drug screening. Due to the stiffness of Markov model for single-cell simulation, it is prone to induce instability by using large time-steps. Hybrid operator splitting (HOS) and uni
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