Sur l'approche mathématique du traitement de l'hépatite virale C par les différences finies non standards [ Mathematical approach of the viral hepatitis C treatment using non-standard finite differences ]

A mathematical modeling of Hepatitis C Virus (HCV) dynamics has been presented in this paper. The proposed model, which involves four coupled ordinary differential equations, describes the interaction of target cells (hepatocytes), infected cells, infectious virions and non-infectious virions. The model takes into consideration the addition of ribavirin to interferon therapy and explains the dynamics regarding biphasic and triphasic decline of viral load in the model. A critical drug efficiency parameter has been defined and it is shown that for efficiencies above this critical value, HCV is eradicated whereas for efficiencies lower this critical value, a new steady state for infectious virions is reached, which is lower than the previous steady state.