Optimality-preserving reduction of controlled chemical reaction networks

Chemical reaction networks (CRNs) are an established population model defined as a system of coupled nonlinear ordinary differential equations across many disciplines. In many applications, for example, in systems biology and epidemiology, CRN parameters such as the kinetic reaction rates can be used as control inputs to steer the system toward a given target. Unfortunately, the resulting optimal control problem is nonlinear, therefore, computationally very challenging. We address this issue by introducing an optimality-preserving reduction algorithm for CRNs. The algorithm partitions the original state variables into a reduced set of macro-variables for which one can define a reduced optimal control problem with provably identical optimal values. The reduction algorithm runs with polynomial time complexity in the size of the CRN. We use this result to reduce verification and control problems of large-scale vaccination models over real-world networks.