Dynamics and application of an epidemiological model for hepatitis C

An epidemiological model for the spread of hepatitis $C$ is developed and discussed. The analysis indicates that the eradication or persistence of the disease is completely determined by the magnitude of the basic reproductive number ${\mathcal{R}}_0$ . The dynamical analysis reveals that the disease free equilibrium of the model is globally asymptotically stable if ${\mathcal{R}}_0$ is less than unity. On the other hand, if ${\mathcal{R}}_0>1$ and the HCV induced death rate is not considered, the unique endemic equilibrium is globally asymptotically stable under certain conditions. Numerical simulations are performed to investigate the influence of different vital parameters on HCV prevalence. Based on the available HCV epidemic data in China, the model is applied to simulate the HCV transmission in the future.