Dynamical Analysis of a Multiscale Model of Hepatitis C Virus Infection Using a Transformed ODEs Model.

Elkaranshawy, Hesham A; Ezzat, Hossam M; Ibrahim, Nermeen N

A mathematically identical ordinary differential equations (ODEs) model was derived from a multiscale partial differential equations (PDEs) model of hepatitis c virus infection, which helps to overcome the limitations of the PDE model in clinical data analysis. We have discussed about basic properties of the system and found the basic reproduction number of the system. A condition for the local stability of the uninfected and the infected steady states is presented. The local stability analysis of the model shows that the system is asymptotically stable at the disease-free equilibrium point when the basic reproduction number is less than one. When the basic reproduction number is greater than one endemic equilibrium point exists, and the local stability analysis proves that this point is asymptotically stable. Numerical sensitivity analysis based on model parameters is performed and therefore the result describes the influence of each parameter on the basic reproduction number.