Global dynamics of a diffusive SEICR HCV model with nonlinear incidences.

To capture the transmission dynamics of hepatitis C virus, we propose and study a reaction–diffusion nonlinear SEICR model, which includes latent, acute, and chronic infection stages. We first establish the well-posedness and boundedness of the model. It is shown the disease-free steady state is globally asymptotically stable if the basic reproduction number R 0 < 1 while the model is uniformly persistent if R 0 > 1. For the special case where the model parameters are spatially homogeneous, we not only derive the explicit expression of R 0 but also show that the positive steady state is globally asymptotically stable if R 0 > 1 through the approach of Lyapunov functionals. The feasibility of the theoretical results is demonstrated by numerical simulations. Moreover, we carry out the sensitivity analysis of R 0 with respect to the parameters and thus the important parameters significantly influencing the dynamic behaviors are identified. [ABSTRACT FROM AUTHOR]