Managing medical equipment capacity with early spread of infection in a region.

We develop a model for a regional decision-maker to analyze the requirement of medical equipment capacity in the early stages of a spread of infections. We use the model to propose and evaluate ways to manage limited equipment capacity. Early-stage infection growth is captured by a stochastic differential equation (SDE) and is part of a two-period community spread and shutdown model. We use the running-maximum process of a geometric Brownian motion to develop a performance metric, probability of breach, for a given capacity level. Decision-maker estimates costs of economy versus health and the time till the availability of a cure; we develop a heuristic rule and an optimal formulation that use these estimates to determine the required medical equipment capacity. We connect the level of capacity to a menu of actions, including the level and timing of shutdown, shutdown effectiveness, and enforcement. Our results show how these actions can compensate for the limited medical equipment capacity in a region. We next address the sharing of medical equipment capacity across regions and its impact on the breach probability. In addition to traditional risk-pooling, we identify a peak-timing effect depending on when infections peak in different regions. We show that equipment sharing may not benefit the regions when capacity is tight. A coupled SDE model captures the messaging coordination and movement across regional borders. Numerical experiments on this model show that under certain conditions, such movement and coordination can synchronize the infection trajectories and bring the peaks closer, reducing the benefit of sharing capacity.