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For a hepatitis C virus (HCV) mathematical model considering host immune system which is studied by Blé et al. (2018), uniform persistence and global asymptotic stability of the endemic equilibrium of the model are considered, and a set of feasible sufficient conditions are obtained by constructing appropriate Lyapunov functions. Our results largely improved those in related works. [ABSTRACT FROM AUTHOR]

We propose a diffusive viral model incorporating cell‐to‐cell infection mode, nonlinear incidences, incubation period, and spatial heterogeneity. For the spatially heterogeneous model, we derive the extinction/persistence result by the basic reproduction number R0. For the spatially homogeneous model, we study global stabilities of steady states by establishing Lyapunov functions. The existing method for studying global stabilities of diffusive viral models has been generalized, which weakens the required conditions. Some existing results can be covered and improved. A specific example is given to illustrate the general results. In addition, we show that R0 is underestimated if we neglect incubation period of infected cells. [ABSTRACT FROM AUTHOR]