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We address the problem of modeling constrained hospital resources in themidst of the COVID-19 pandemic in order to inform decision-makers of futuredemand and assess the societal value of possible interventions. For broadapplicability, we focus on the common yet challenging scenario wherepatient-level data for a region of interest are not available. Instead, givendaily admissions counts, we model aggregated counts of observed resource use,such as the number of patients in the general ward, in the intensive care unit,or on a ventilator. In order to explain how individual patient trajectoriesproduce these counts, we propose an aggregate count explicit-duration hiddenMarkov model, nicknamed the ACED-HMM, with an interpretable, compactparameterization. We develop an Approximate Bayesian Computation approach thatdraws samples from the posterior distribution over the model's transition andduration parameters given aggregate counts from a specific location, thusadapting the model to a region or individual hospital site of interest. Samplesfrom this posterior can then be used to produce future forecasts of any countsof interest. Using data from the United States and the United Kingdom, we showour mechanistic approach provides competitive probabilistic forecasts for thefuture even as the dynamics of the pandemic shift. Furthermore, we show how ourmodel provides insight about recovery probabilities or length of staydistributions, and we suggest its potential to answer challenging what-ifquestions about the societal value of possible interventions.

Approximate Bayesian Computation for an Explicit-Duration Hidden Markov Model of COVID-19 Hospital Trajectories