Publications

This report documents a statistical method for the "real-time" characterization of partially observed epidemics. Observations consist of daily counts of symptomatic patients, diagnosed with the disease. Characterization, in this context, refers to estimation of epidemiological parameters that can be used to provide short-term forecasts of the ongoing epidemic, as well as to provide gross information for the time-dependent infection rate. The characterization problem is formulated as a Bayesian inverse problem, and is predicated on a model for the distribution of the incubation period. The model parameters are estimated as distributions using a Markov Chain Monte Carlo (MCMC) method, thus quantifying the uncertainty in the estimates. The method is applied to the COVID-19 pandemic of 2020, using data at the country, provincial (e.g., states) and regional (e.g. county) levels. The epidemiological model includes a stochastic component due to uncertainties in the incubation period. This model-form uncertainty is accommodated by a pseudo-marginal Metropolis-Hastings MCMC sampler, which produces posterior distributions that reflect this uncertainty. We approximate the discrepancy between the data and the epidemiological model using Gaussian and negative binomial error models; the latter was motivated by the over-dispersed count data. For small daily counts we find the performance of the calibrated models to be similar for the two error models. For large daily counts the negative-binomial approximation is numerically unstable unlike the Gaussian error model. Application of the model at the country level (for the United States, Germany, Italy, etc.) generally provided accurate forecasts, as the data consisted of large counts which suppressed the day-to-day variations in the observations. Further, the bulk of the data is sourced over the duration before the relaxation of the curbs on population mixing, and is not confounded by any discernible country-wide second wave of infections. At the state-level, where reporting was poor or which evinced few infections (e.g., New Mexico), the variance in the data posed some, though not insurmountable, difficulties, and forecasts were able to capture the data with large uncertainty bounds. The method was found to be sufficiently sensitive to discern the flattening of the infection and epidemic curve due to shelter-in-place orders after around 90% quantile for the incubation distribution (about 10 days for COVID-19). The proposed model was also used at a regional level to compare the forecasts for the central and north-west regions of New Mexico. Modeling the data for these regions illustrated different disease spread dynamics captured by the model. While in the central region the daily counts peaked in the late April, in the north-west region the ramp-up continued for approximately three more weeks.

In March and April of 2020 there was widespread concern about availability of medical resources required to treat Covid-19 patients who become seriously ill. A simulation model of supply management was developed to aid understanding of how to best manage available supplies and channel new production. Forecasted demands for critical therapeutic resources have tremendous uncertainty, largely due to uncertainties about the number and timing of patient arrivals. It is therefore essential to evaluate any process for managing supplies in view of this uncertainty. To support such evaluations, we developed a modeling framework that would allow an integrated assessment in the context of uncertainty quantification. At the time of writing there has been no need to execute this framework because adaptations of the medical system have been able to respond effectively to the outbreak. This report documents the framework and its implemented components should need later arise for its application.

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As part of the Department of Energy response to the novel coronavirus pandemic of 2020, a modeling effort was sponsored by the DOE Office of Science. One task of this modeling effort at Sandia was to develop a model to predict medical resource needs given various patient arrival scenarios. Resources needed include personnel resources (nurses, ICU nurses, physicians, respiratory therapists), fixed resources (regular or ICU beds and ventilators), and consumable resources (masks, gowns, gloves, face shields, sedatives). This report documents the uncertainty analysis that was performed on the resource model. The uncertainty analysis involved sampling 26 input parameters to the model. The sampling was performed conditional on the patient arrival streams that also were inputs to the model. These patient arrival streams were derived from various epidemiology models and had a significant effect on the projected resource needs. In this report, we document the sampling approach, the parameter ranges used, and the computational workflow necessary to perform large-scale uncertainty studies for every county and state in the United States.

Abstract not provided.