Dynamics of hepatitis C virus infection: Mathematical modeling and parameter estimation

In this paper, we provide a differential mathematical model with non-integer order derivative (fractional-order) to investigate the dynamics of Hepatitis-C Virus (HCV) replication, in presence of interferon-(IFN) treatment. The fractional-order is considered to represent the intermediate cellular interactions and intracellular delay of the viral life cycle. We mathe- matically analyze and characterize the steady states and dynamical behavior of the model in presence of interferon- treatment. We deduce a threshold parameter R (average number of newly infected cells produced by a single infected cell) in terms of the treatment effcacy pa- rameter 0 1 and other parameters. We also provide a numerical technique for solving the fractional-order model and fitting the model to real data during treatment. The numerical simulations con-rm that the fractional-order differential models have the ability to provide ac- curate descriptions of nonlinear biological systems with memory. The analyses presented here give an insight to understand the dynamics of HCV infection.