Fractional-order delay differential equations for the dynamics of hepatitis C virus infection with IFN-α treatment

Herein, we propose a fractional-order delay differential model for the dynamics of Hepatitis-C Virus (HCV), with interferon-α(IFN-α) treatment. A fractional-order derivative is considered to represent the long-run immune memory required for intermediate cellular interactions. A discrete time-delay τ is also incorporated to represent the intracellular delay between initial infection of a cell by HCV and the release of new virions. By using time-delay τ as a bifurcation parameter, the stability of infection-free and infected steady states is investigated. The coefficients of the corresponding characteristic equation depend on τ, and geometric stability switch criteria is used to study the stability switching properties. The fractional-order delay differential model has been verified with real observations. Incorporating fractional-order and immune memory, in the model, greatly enriches the dynamics of the system and improves the consistency of the model with the observations.