Dynamics of hepatitis C virus infection: mathematical modeling and parameter estimation. (English) Zbl 1385.34037
Summary: 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-\(\alpha\) (IFN) treatment. The fractional-order is considered to represent the intermediate cellular interactions and intracellular delay of the viral life cycle. We mathematically analyze and characterize the steady states and dynamical behavior of the model in presence of interferon-\(\alpha\) treatment. We deduce a threshold parameter \(\operatorname{Re}_0\) (average number of newly infected cells produced by a single infected cell) in terms of the treatment efficacy parameter \(0\leq \varepsilon < 1\) 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 confirm that the fractional-order differential models have the ability to provide accurate descriptions of nonlinear biological systems with memory. The analyses presented here give an insight to understand the dynamics of HCV infection.
MSC:
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 34A08 | Fractional ordinary differential equations |
| 92C60 | Medical epidemiology |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
| 34D20 | Stability of solutions to ordinary differential equations |
Keywords:
fractional calculus; hepatitis C virus; interferon-\(\alpha\); parameter estimation; viral dynamics models; stabilityReferences:
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