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
