Chance-constrained stochastic optimal control of epidemic models: A fourth moment method-based reformulation

This work proposes a methodology for the reformulation of chance-constrained stochastic optimal control problems that ensures reliable uncertainty management of epidemic outbreaks. Specifically, the chance constraints are reformulated in terms of the first four moments of the stochastic state variables through the so-called fourth moment method for reliability. Moreover, a spectral technique is employed to obtain surrogate models of the stochastic state variables, which enables the efficient computation of the required statistics. The practical implementation of the proposed approach is demonstrated via the optimal control of two different stochastic mathematical models of the COVID-19 transmission. The numerical experiments confirm that, unlike those reformulations based on the Chebyshev-Cantelli's inequality, the proposed method does not exhibit the undesired outcomes that are typically observed when a higher precision is required for the risk level associated to the given chance constraints.