Reverse engineering combination therapies for evolutionary dynamics of disease: An ℌ∞ approach

We propose a general algorithm for the systematic design of feedback strategies to stabilize the evolutionary dynamics of a generic disease model using an H_∞ approach. We show that designing therapy concentrations can be cast as an H_∞ state feedback synthesis problem, where the feedback gain is constrained to not only be strictly diagonal, but also that its diagonal elements satisfy an overdetermined set of linear equations. Leveraging recent results in positive systems, we develop an algorithm that always yields a stabilizing controller.