Abstract
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 R0<1 while the model is uniformly persistent if R0>1. For the special case where the model parameters are spatially homogeneous, we not only derive the explicit expression of R0 but also show that the positive steady state is globally asymptotically stable if R0>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 R0 with respect to the parameters and thus the important parameters significantly influencing the dynamic behaviors are identified.
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