Daily Forecasting of New Cases for Regional Epidemics of Coronavirus Disease 2019 with Bayesian Uncertainty Quantification

Abstract

To increase situational awareness and support evidence-based policy-making, we formulated two types of mathematical models for COVID-19 transmission within a regional population. One is a fitting function that can be calibrated to reproduce an epidemic curve with two timescales (e.g., fast growth and slow decay). The other is a compartmental model that accounts for quarantine, self-isolation, social distancing, a non-exponentially distributed incubation period, asymptomatic individuals, and mild and severe forms of symptomatic disease. Using Bayesian inference, we have been calibrating our models daily for consistency with new reports of confirmed cases from the 15 most populous metropolitan statistical areas in the United States and quantifying uncertainty in parameter estimates and predictions of future case reports. This online learning approach allows for early identification of new trends despite considerable variability in case reporting. We infer new significant upward trends for five of the metropolitan areas starting between 19-April-2020 and 12-June-2020.

Data-driven Optimized Control of the COVID-19 Epidemics

“…These I max values are a ratio of ICU beds to the population of people which require them. Following [21], we estimate that the probability of death conditioned on symptomatic infection is equal to f H × (1 − f R ) = 0.01134, where the two parameters f H and f R were independently computed in [29] and [32], respectively. Data [30, 14] shows that the mortality rate for patients sent to ICU is between 30% and 40%, thus, it is reasonable to assume that an overall fraction of infected people equal to 0.01134/0.35 = 0.0324 needs ICU beds.…”

“…The relative infectiousness μ is set at 0.9 [42], and the fraction of the symptomatic population is set at 0.64 [2, 35]. The parametrization of γ I , γ A , μ , and σ are consistent with a more complex model which was used to perform daily forecasts of the disease spread [21]. We assume p test = 0.25 and p sq = 0.4, noting that these parameters were able to reproduce the infected population at the time of the inference (we estimated that about 15 to 20% of the total population infected in the New York City MSA on 07-Jul-2020 when we parametrize the model.…”

“…The time at which we perform the inference is t 4 , which is also the time after which optimization of the control action begins. The two-phase piecewise linear model is the minimal model that we found capable to reproduce the data, and can be validated by more rigorous model-selection procedure detailed in [21].…”

“…We thus set a rough estimation for λ to be 1 / 3 (d). In a more complex model with multiple stages of the disease progression [23], one could account for the fact that a patient can be both pre-symptomatic and infectious. The coefficients γ I and γ A , which are the transition rate to recovery of the symptomatic and asymptomatic populations, are estimated to be 0.12 (1/d) [47] and 0.26 (1/d) [39].…”

“…The model is structurally similar to the models analyzed in Refs. [6, 21], but simplified to allow for efficient calculations of optimal control solutions. Figure 1 illustrates a schematic diagram of the model.…”