A Scalable Formulation for Engineering Combination Therapies for Evolutionary Dynamics of Disease

It has been shown that optimal controller synthesis for positive systems can be formulated as a linear program. Leveraging these results, we propose a scalable iterative algorithm for the systematic design of sparse, small gain feedback strategies that stabilize the evolutionary dynamics of a generic disease model. We achieve the desired feedback structure by augmenting the optimization problems with {ell}1 and {ell}2 regularization terms, and illustrate our method on an example inspired by an experimental study aimed at finding appropriate HIV neutralizing antibody therapy combinations in the presence of escape mutants.