Input-output approaches for personalized drug dosing of antibiotics

The aim of this chapter is to report analytical and individual-based methods for antibiotic dose selection that are based on tools from system and control theory. A brief system analysis of standard population pharmacokinetic models proves that such models are nonnegative and stable. Then, an input-output analysis leads to an open-loop control law which yields a dosing for the average patient, based on the equilibrium trajectory of the system. This approach is then incorporated into a “worst-case” analysis based on the monotony of the state trajectories with respect to the clearance (model parameter). Finally, a heuristic method of an estimated state feedback is presented. These methods were successively illustrated by numerical simulations on a model describing the pharmacokinetics of meropenem, an intravenous antibiotic for treatment of severe sepsis.