Global dynamics of a general degenerate multiscale age-structured HCV diffusive model with spatial heterogeneity

In this paper, a general degenerate multiscale HCV diffusive model with spatial heterogeneity was established and analyzed. We derived the variational formula of the basic reproduction number $ {{\Re }_{0}} $. The existence of positive nonhomogeneous equilibrium was demonstrated through proving the uniform persistence of the model when $ {{\Re }_{0}}>1 $. Through constructing the Lyapunov function, the global asymptotic stability of the disease-free nonhomogeneous equilibrium was demonstrated if $ {{\Re }_{0}}<1 $, and the global asymptotic stability of the positive nonhomogeneous equilibrium was demonstrated if $ {{\Re }_{0}}>1 $. Numerical simulations were consistent with theoretical analysis. The simulations also show that infection risk may increase with increasing spatial heterogeneity intensity.