Mathematical modelling of hepatitis C virus dynamics response to therapeutic effects of interferon and ribavirin

Abstract

This paper aims at designing a two compartmental mathematical model for determining the response of protein (Interferon) and drug (Ribarivin) for a patient who is suffering from hepatitis C virus (HCV). The stability of developed mathematical model is established. Using inverse techniques, model parameters and functions are identified. To test efficiency and response to interferon and ribavirin as HCV treatment, the validation of the mathematical model is achieved by considering a patient on treatment during 12 months. The results obtained are rather satisfactory since model parameters vary around their corresponding value that is equilibrium values for healthy subjects. Furthermore, the reaction of the disease to treatment can be modelled and a feedback can be approximated by the solution of an optimal control problem. The increasing necessity to interpret the meaning of measurable variables such as interferon and ribavirin under both physiological and pathological conditions for a patient has imposed the need for relatively simple models that should be able to describe as accurately as possible the mechanical behaviour of the disease.