Time-varying Pharmacodynamics in a Simple Non-Integer HIV Infection Model

In this paper we study the effect of time-varying drug exposure in the dynamics of a fractional order model for the human immunodeficiency virus infection. We compute the reproduction number of the model and verify the stability of the disease-free equilibrium. The model is simulated for parameters directly modelling the pharmacodynamics of HIV, namely the slope of the dose-response curve, the drug's half-life, and the dosing interval. The later affect in a significant way the infection patterns. The order of the fractional derivative is also a key player of the model, adding more information, which could be useful for a deeper understanding of the pharmacodynamics of HIV, necessary for more accurate therapeutic regimens.