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

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Vanessa Jonsson and Richard M. Murray
Submitted, 2014 American Control Conference (ACC)

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 algo- rithm 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 `1 and `2 regular- ization 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.