ICU capacity expansion under uncertainty in the early stages of a pandemic

We propose a general modular approach to support decision-makers' response in the early stages of a pandemic with resource expansion, motivated by the shortage of Covid-19-related intensive care units (ICU) capacity in 2020 in Italy. Our approach uses (1) a stochastic extension of an epidemic model for scenarios of projected infections, (2) a capacity load model to translate infections into scenarios of demand for the resources of interest, and (3) an optimization model to allocate this demand to the projected levels of resources based on different values of investment. We demonstrate this approach with the onset of the first and second Covid-19 waves in three Italian regions, using the data available at that time. For epidemic modeling, we used a parsimonious stochastic susceptible-infected-removed (SIR) model with a robust estimation procedure based on bootstrap resampling, suitable for a noisy and data-limited environment. For capacity loading, we used a Cox queuing model to translate the projected infections into demand for ICU, using stochastic intensity to capture the variability of the patient arrival process. Finally, we used stochastic dynamic optimization to select the best policy (when and how much to expand) to minimize the expected number of patients denied ICU for any level of investment in capacity expansion and obtain an efficient frontier. The frontier allows a trade-off between investment in additional resources and the number of patients denied intensive care. Moreover, in the panic-driven early days of a pandemic, decision-makers can also obtain the time until which they can postpone action, potentially reducing investment costs without increasing the expected number of denied patients.