MATHEMATICAL MODELING OF HEPATITIS C VIRAL KINETICS

Abstract

In this thesis, we propose a mathematical model of Hepatitis C Virus (HCV) dynamics and antiviral therapy, consisting of four coupled ordinary differential equations, describing 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 a biphasic and triphasic decline of viral load in the model. A critical drug efficacy parameter has been defined and it is shown that for an efficacy above this critical value, HCV is eradicated whereas for efficacy lower this critical value, a new steady state for infectious virions is reached, which is lower than the previous steady state value. Next, we consider various combinations of proliferation terms, including a saturation incidence rate and formulate mathematical models of HCV. Their dynamics are studied and the results compared. Since, in viral dynamics, the time for viral infection is not instantaneous, we incorporate a discrete time delay induced model for hepatitis C virus incorporating the healthy and infected hepatocytes as well as infectious and non-infectious virions. This model is validated using 12 patient data obtained from the study, conducted at the University of Sao Paulo Hospital das clinicas. We also apply optimal control to HCV model to maximize uninfected hepatocytes, minimize the infected hepatocytes and viral load such that an optimal control pair of efficacy of the drugs can be obtained, minimizing the side effects of the drugs