Time-varying pharmacodynamics in a simple non-integer HIV infection model

•the effect of time-varying drug exposure in HIV infected patients is studied in a fractional order model.•the slope of the dose-response curve, the drug’s half-life, and the dosing interval impact significantly the dynamics of the proposed model.•the order of the fractional derivative can be used to deepen the understanding of the pharmacodynamics of HIV, necessary for more accurate therapeutic regimens. 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.