Correction: Inferring school district learning modalities during the COVID-19 pandemic with a hidden Markov model.

[This corrects the article DOI: 10.1371/journal.pone.0292354.].

Inferring school district learning modalities during the COVID-19 pandemic with a hidden Markov model.

During the COVID-19 pandemic, many public schools across the United States shifted from fully in-person learning to alternative learning modalities such as hybrid and fully remote learning. In this study, data from 14,688 unique school districts from August 2020 to June 2021 were collected to track changes in the proportion of schools offering fully in-person, hybrid and fully remote learning over time. These data were provided by Burbio, MCH Strategic Data, the American Enterprise Institute's Return to Learn Tracker and individual state dashboards. Because the modalities reported by these sources were incomplete and occasionally misaligned, a model was needed to combine and deconflict these data to provide a more comprehensive description of modalities nationwide. A hidden Markov model (HMM) was used to infer the most likely learning modality for each district on a weekly basis. This method yielded higher spatiotemporal coverage than any individual data source and higher agreement with three of the four data sources than any other single source. The model output revealed that the percentage of districts offering fully in-person learning rose from 40.3% in September 2020 to 54.7% in June of 2021 with increases across 45 states and in both urban and rural districts. This type of probabilistic model can serve as a tool for fusion of incomplete and contradictory data sources in order to obtain more reliable data in support of public health surveillance and research efforts.

Gecko: A time-series model for COVID-19 hospital admission forecasting.

During the COVID-19 pandemic, concerns about hospital capacity in the United States led to a demand for models that forecast COVID-19 hospital admissions. These short-term forecasts were needed to support planning efforts by providing decision-makers with insight about future demands for health care capacity and resources. We present a SARIMA time-series model called Gecko developed for this purpose. We evaluate its historical performance using metrics such as mean absolute error, predictive interval coverage, and weighted interval scores, and compare to alternative hospital admission forecasting models. We find that Gecko outperformed baseline approaches and was among the most accurate models for forecasting hospital admissions at the state and national levels from January-May 2021. This work suggests that simple statistical methods can provide a viable alternative to traditional epidemic models for short-term forecasting.

Trends in Disease Severity and Health Care Utilization During the Early Omicron Variant Period Compared with Previous SARS-CoV-2 High Transmission Periods - United States, December 2020-January 2022.

The B.1.1.529 (Omicron) variant of SARS-CoV-2, the virus that causes COVID-19, was first clinically identified in the United States on December 1, 2021, and spread rapidly. By late December, it became the predominant strain, and by January 15, 2022, it represented 99.5% of sequenced specimens in the United States* (1). The Omicron variant has been shown to be more transmissible and less virulent than previously circulating variants (2,3). To better understand the severity of disease and health care utilization associated with the emergence of the Omicron variant in the United States, CDC examined data from three surveillance systems and a large health care database to assess multiple indicators across three high-COVID-19 transmission periods: December 1, 2020-February 28, 2021 (winter 2020-21); July 15-October 31, 2021 (SARS-CoV-2 B.1.617.2 [Delta] predominance); and December 19, 2021-January 15, 2022 (Omicron predominance). The highest daily 7-day moving average to date of cases (798,976 daily cases during January 9-15, 2022), emergency department (ED) visits (48,238), and admissions (21,586) were reported during the Omicron period, however, the highest daily 7-day moving average of deaths (1,854) was lower than during previous periods. During the Omicron period, a maximum of 20.6% of staffed inpatient beds were in use for COVID-19 patients, 3.4 and 7.2 percentage points higher than during the winter 2020-21 and Delta periods, respectively. However, intensive care unit (ICU) bed use did not increase to the same degree: 30.4% of staffed ICU beds were in use for COVID-19 patients during the Omicron period, 0.5 percentage points lower than during the winter 2020-21 period and 1.2 percentage points higher than during the Delta period. The ratio of peak ED visits to cases (event-to-case ratios) (87 per 1,000 cases), hospital admissions (27 per 1,000 cases), and deaths (nine per 1,000 cases [lagged by 3 weeks]) during the Omicron period were lower than those observed during the winter 2020-21 (92, 68, and 16 respectively) and Delta (167, 78, and 13, respectively) periods. Further, among hospitalized COVID-19 patients from 199 U.S. hospitals, the mean length of stay and percentages who were admitted to an ICU, received invasive mechanical ventilation (IMV), and died while in the hospital were lower during the Omicron period than during previous periods. COVID-19 disease severity appears to be lower during the Omicron period than during previous periods of high transmission, likely related to higher vaccination coverage,† which reduces disease severity (4), lower virulence of the Omicron variant (3,5,6), and infection-acquired immunity (3,7). Although disease severity appears lower with the Omicron variant, the high volume of ED visits and hospitalizations can strain local health care systems in the United States, and the average daily number of deaths remains substantial.§ This underscores the importance of national emergency preparedness, specifically, hospital surge capacity and the ability to adequately staff local health care systems. In addition, being up to date on vaccination and following other recommended prevention strategies are critical to preventing infections, severe illness, or death from COVID-19.

COVID-19-Related School Closures and Learning Modality Changes - United States, August 1-September 17, 2021.

Beginning in January 2021, the U.S. government prioritized ensuring continuity of learning for all students during the COVID-19 pandemic (1). To estimate the extent of COVID-19-associated school disruptions, CDC and the Johns Hopkins University Applied Physics Laboratory used a Hidden Markov Model (HMM) (2) statistical approach to estimate the most likely actual learning modality based on patterns observed in past data, accounting for conflicting or missing information and systematic Internet searches (3) for COVID-19-related school closures. This information was used to assess how many U.S. schools were open, and in which learning modalities, during August 1-September 17, 2021. Learning modalities included 1) full in-person learning, 2) a hybrid of in-person and remote learning, and 3) full remote learning.

Pediatric COVID-19 Cases in Counties With and Without School Mask Requirements - United States, July 1-September 4, 2021.

Consistent and correct mask use is a critical strategy for preventing the transmission of SARS-CoV-2, the virus that causes COVID-19 (1). CDC recommends that schools require universal indoor mask use for students, staff members, and others in kindergarten through grade 12 (K-12) school settings (2). As U.S. schools opened for the 2021-22 school year in the midst of increasing community spread of COVID-19, some states, counties, and school districts implemented mask requirements in schools. To assess the impact of masking in schools on COVID-19 incidence among K-12 students across the United States, CDC assessed differences between county-level pediatric COVID-19 case rates in schools with and without school mask requirements.

Real-world Effect of Monoclonal Antibody Treatment in COVID-19 Patients in a Diverse Population in the United States.

BACKGROUND: Monoclonal antibodies (mAbs) against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) are a promising treatment for limiting the progression of coronavirus disease 2019 (COVID-19) and decreasing strain on hospitals. Their use, however, remains limited, particularly in disadvantaged populations. METHODS: Electronic health records were reviewed from SARS-CoV-2 patients at a single medical center in the United States that initiated mAb infusions in January 2021 with the support of the US Department of Health and Human Services' National Disaster Medical System. Patients who received mAbs were compared with untreated patients from the time period before mAb availability who met eligibility criteria for mAb treatment. We used logistic regression to measure the effect of mAb treatment on the risk of hospitalization or emergency department (ED) visit within 30 days of laboratory-confirmed COVID-19. RESULTS: Of 598 COVID-19 patients, 270 (45%) received bamlanivimab and 328 (55%) were untreated. Two hundred thirty-one patients (39%) were Hispanic. Among treated patients, 5/270 (1.9%) presented to the ED or required hospitalization within 30 days of a positive SARS-CoV-2 test, compared with 39/328 (12%) untreated patients (P < .001). After adjusting for age, gender, and comorbidities, the risk of ED visit or hospitalization was 82% lower in mAb-treated patients compared with untreated patients (95% CI, 56%-94%). CONCLUSIONS: In this diverse, real-world COVID-19 patient population, mAb treatment significantly decreased the risk of subsequent ED visit or hospitalization. Broader treatment with mAbs, including in disadvantaged patient populations, can decrease the burden on hospitals and should be facilitated in all populations in the United States to ensure health equity.

Can subjective pain be inferred from objective physiological data? Evidence from patients with sickle cell disease.

Patients with sickle cell disease (SCD) experience lifelong struggles with both chronic and acute pain, often requiring medical interventMaion. Pain can be managed with medications, but dosages must balance the goal of pain mitigation against the risks of tolerance, addiction and other adverse effects. Setting appropriate dosages requires knowledge of a patient's subjective pain, but collecting pain reports from patients can be difficult for clinicians and disruptive for patients, and is only possible when patients are awake and communicative. Here we investigate methods for estimating SCD patients' pain levels indirectly using vital signs that are routinely collected and documented in medical records. Using machine learning, we develop both sequential and non-sequential probabilistic models that can be used to infer pain levels or changes in pain from sequences of these physiological measures. We demonstrate that these models outperform null models and that objective physiological data can be used to inform estimates for subjective pain.

Model reconstruction from temporal data for coupled oscillator networks.

In a complex system, the interactions between individual agents often lead to emergent collective behavior such as spontaneous synchronization, swarming, and pattern formation. Beyond the intrinsic properties of the agents, the topology of the network of interactions can have a dramatic influence over the dynamics. In many studies, researchers start with a specific model for both the intrinsic dynamics of each agent and the interaction network and attempt to learn about the dynamics of the model. Here, we consider the inverse problem: given data from a system, can one learn about the model and the underlying network? We investigate arbitrary networks of coupled phase oscillators that can exhibit both synchronous and asynchronous dynamics. We demonstrate that, given sufficient observational data on the transient evolution of each oscillator, machine learning can reconstruct the interaction network and identify the intrinsic dynamics.

Continuous Pain Assessment Using Ensemble Feature Selection from Wearable Sensor Data.

Sickle cell disease (SCD) is a red blood cell disorder complicated by lifelong issues with pain. Management of SCD related pain is particularly challenging due to its subjective nature. Hence, the development of an objective automatic pain assessment method is critical to pain management in SCD. In this work, we developed a continuous pain assessment model using physiological and body movement sensor signals collected from a wearable wrist-worn device. Specifically, we implemented ensemble feature selection methods to select robust and stable features extracted from wearable data for better understanding of pain. Our experiments showed that the stability of feature selection methods could be substantially increased by using the ensemble approach. Since different ensemble feature selection methods prefer varying feature subsets for pain estimation, we further utilized stacked generalization to maximize the information usage contained in the selected features from different methods. Using this approach, our best performing model obtained the root-mean-square error of 1.526 and the Pearson correlation of 0.618 for continuous pain assessment. This indicates that subjective pain scores can be estimated using objective wearable sensor data with high precision.

Chaos in Kuramoto oscillator networks.

Kuramoto oscillators are widely used to explain collective phenomena in networks of coupled oscillatory units. We show that simple networks of two populations with a generic coupling scheme, where both coupling strengths and phase lags between and within populations are distinct, can exhibit chaotic dynamics as conjectured by Ott and Antonsen [Chaos 18, 037113 (2008)]. These chaotic mean-field dynamics arise universally across network size, from the continuum limit of infinitely many oscillators down to very small networks with just two oscillators per population. Hence, complicated dynamics are expected even in the simplest description of oscillator networks.

Chimera states in two populations with heterogeneous phase-lag.

The simplest network of coupled phase-oscillators exhibiting chimera states is given by two populations with disparate intra- and inter-population coupling strengths. We explore the effects of heterogeneous coupling phase-lags between the two populations. Such heterogeneity arises naturally in various settings, for example, as an approximation to transmission delays, excitatory-inhibitory interactions, or as amplitude and phase responses of oscillators with electrical or mechanical coupling. We find that breaking the phase-lag symmetry results in a variety of states with uniform and non-uniform synchronization, including in-phase and anti-phase synchrony, full incoherence (splay state), chimera states with phase separation of 0 or π between populations, and states where both populations remain desynchronized. These desynchronized states exhibit stable, oscillatory, and even chaotic dynamics. Moreover, we identify the bifurcations through which chimeras emerge. Stable chimera states and desynchronized solutions, which do not arise for homogeneous phase-lag parameters, emerge as a result of competition between synchronized in-phase, anti-phase equilibria, and fully incoherent states when the phase-lags are near ±π2 (cosine coupling). These findings elucidate previous experimental results involving a network of mechanical oscillators and provide further insight into the breakdown of synchrony in biological systems.

Chimera states in networks of phase oscillators: The case of two small populations.

Chimera states are dynamical patterns in networks of coupled oscillators in which regions of synchronous and asynchronous oscillation coexist. Although these states are typically observed in large ensembles of oscillators and analyzed in the continuum limit, chimeras may also occur in systems with finite (and small) numbers of oscillators. Focusing on networks of 2N phase oscillators that are organized in two groups, we find that chimera states, corresponding to attracting periodic orbits, appear with as few as two oscillators per group and demonstrate that for N>2 the bifurcations that create them are analogous to those observed in the continuum limit. These findings suggest that chimeras, which bear striking similarities to dynamical patterns in nature, are observable and robust in small networks that are relevant to a variety of real-world systems.

Chimera states on the surface of a sphere.

A chimera state is a spatiotemporal pattern in which a network of identical coupled oscillators exhibits coexisting regions of asynchronous and synchronous oscillation. Two distinct classes of chimera states have been shown to exist: "spots" and "spirals." Here we study coupled oscillators on the surface of a sphere, a single system in which both spot and spiral chimera states appear. We present an analysis of the birth and death of spiral chimera states and show that although they coexist with spot chimeras, they are stable in disjoint regions of parameter space.

Symmetry breaking in optimal timing of traffic signals on an idealized two-way street.

Simple physical models based on fluid mechanics have long been used to understand the flow of vehicular traffic on freeways; analytically tractable models of flow on an urban grid, however, have not been as extensively explored. In an ideal world, traffic signals would be timed such that consecutive lights turned green just as vehicles arrived, eliminating the need to stop at each block. Unfortunately, this "green-wave" scenario is generally unworkable due to frustration imposed by competing demands of traffic moving in different directions. Until now this has typically been resolved by numerical simulation and optimization. Here, we develop a theory for the flow in an idealized system consisting of a long two-way road with periodic intersections. We show that optimal signal timing can be understood analytically and that there are counterintuitive asymmetric solutions to this signal coordination problem. We further explore how these theoretical solutions degrade as traffic conditions vary and automotive density increases.

Chimera states on a flat torus.

Chimera states are surprising spatiotemporal patterns in which regions of coherence and incoherence coexist. Initially observed numerically, these mathematical oddities were recently reproduced in a laboratory setting, sparking a flurry of interest in their properties. Here we use asymptotic methods to derive the conditions under which two-dimensional "spot" and "stripe" chimeras (similar to those observed in experiments) can exist in a periodic space. We also discover a previously unobserved asymmetric chimera state, whose existence plays a major role in determining when other chimera states are observable in experiment and simulation. Finally, we use numerical methods to verify theoretical predictions and determine which states are dynamically stable.

A model balancing cooperation and competition can explain our right-handed world and the dominance of left-handed athletes.

An overwhelming majority of humans are right-handed. Numerous explanations for individual handedness have been proposed, but this population-level handedness remains puzzling. Here, we present a novel mathematical model and use it to test the idea that population-level hand preference represents a balance between selective costs and benefits arising from cooperation and competition in human evolutionary history. We use the selection of elite athletes as a test-bed for our evolutionary model and find evidence for the validity of this idea. Our model gives the first quantitative explanation for the distribution of handedness both across and within many professional sports. It also predicts strong lateralization of hand use in social species with limited combative interaction, and elucidates the absence of consistent population-level 'pawedness' in some animal species.