Across many disciplines, chemical reaction networks (CRNs) are an established
population model defined as a system of coupled nonlinear ordinary differential
equations. 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 from which one can exactly recover the solution
of the original control problem. Notably, the reduction algorithm runs with
polynomial time complexity in the size of the CRN. We use this result to reduce
reachability and control problems of large-scale protein-interaction networks
and vaccination models with hundreds of thousands of state variables