Fractional complex-order model for HIV infection with drug resistance during therapy

Abstract

We propose a fractional complex-order model for drug resistance in HIV infection. We consider three distinct growth rates for the CD4⁺ T helper cells. We simulate the model for different values of the fractional derivative of complex order D^α±jβ, where α,β ∈  R ⁺, and for distinct growth rates. The fractional derivative of complex order is a generalization of the integer-order derivative where α = 1 and β = 0. The fractional complex-order system reveals rich dynamics and variation of the value of the complex-order derivative sheds new light on the modeling of the intracellular delay. Additionally, fractional patterns are characterized by time responses with faster transients and slower evolutions towards the steady state.