Synthesizing Combination Therapies for Evolutionary Dynamics of Disease for Nonlinear Pharmacodynamics

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Vanessa Jonsson, Nikolai Matni and Richard M. Murray
2014 Conference on Decision and Control (CDC)

Our previous results proposed an iterative scalable algorithm for the systematic design of sparse, small gain feedback strategies that stabilize the evolutionary dynamics of a generic disease model with linear pharmacodynamics. Here we use piecewise linear approximations to model the nonlinear drug effects and leverage results from optimal controller synthesis for positive systems to formulate the feedback synthesis problem as an optimization problem that sequentially explores piecewise linear subsystems corresponding to higher and higher treatment dosages.