Optimal Safety-Critical Control of Epidemics

We present a generalized model for epidemic processes that partitions control into changes in linear and non-linear flow rates between compartments, respectively. We then define an optimal control problem that minimizes the weighted cost of rate control on the generalized model while maintaining conditions that guarantee system safety at any time using control barrier functions. Using this formulation, we prove that under homogeneous penalties the optimal controller will always favor increasing the linear flow out of an infectious process over reducing nonlinear flow in. Further, in the case of heterogeneous penalties, we provide necessary and sufficient conditions under which the optimal controller will set control of non-linear rates (i.e., the reduction of flow rate into the infection process) to zero. We then illustrate these results through the simulation of a bi-virus SEIQRS model.