Figure 2. Optimal ventilator stockpiles for a mild pandemic scenario, Texas, USA. The total size of the optimal stockpile, summed across the central and 8 HSR stockpiles, decreases as risk tolerance increases. Risk for unmet demand for ventilators is quantified as the expected number of hospitalized influenza patients statewide not receiving necessary ventilation (EUD) (A) and the probability of at least 1 hospitalized patient in Texas not receiving necessary ventilation (PUD) (B). We optimized directly for EUD and calculated PUD post hoc. Red circles indicate EUD/PUD of 5 patients. C) Optimal allocation among central and regional sites when EUD is set to 5 patients, equivalent to a stockpile of 272 ventilators. EUD, expected unmet demand; PUD, probability of unmet demand; HSR, health service region.