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In this paper, a mathematical analysis of the global dynamics of a partialdifferential equation viral infection cellular model is carried out. We studythe dynamics of a hepatitis C virus (HCV) model, under therapy, that considersboth absorption phenomenon and diffusion of virions, infected and uninfectedcells in liver. Firstly, we prove boundedness of the potential solutions,global existence, uniqueness and positivity of the solutions to the obtainedinitial value and boundary problem. Then, the dynamical behavior of the modelis completely determined by a threshold parameter called the basic reproductionnumber $\mathcal{R}_{0}$. We show that the uninfected spatially homogeneousequilibrium of the model is globally asymptotically stable if $\mathcal{R}_{0}\leq 1 $ by using the direct Lyapunov method. This means that the HCV iscleared and the disease dies out. Also, the global asymptotically propertiesstability of the infected spatially homogeneous equilibrium of the model arestudied via a skilful construction of a suitable Lyapunov functional. It meansthat the HCV persists in the host and the infection becomes chronic. Finally,numerical simulations are performed to support the theoretical resultsobtained.

Global analysis of a spatiotemporal cellular model for the transmission of hepatitis C virus with Hattaf-Yousfi functional response