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As of November 2020, the number of COVID-19 cases was increasing rapidly in many countries. In Europe, the virus spread slowed considerably in the late spring due to strict lockdown, but a second wave of the pandemic grew throughout the fall. In this study, we first reconstruct the time evolution of the effective reproduction numbers R(t) for each country by integrating the equations of the classic Susceptible-Infectious-Recovered (SIR) model. We cluster countries based on the estimated R(t) through a suitable time series dissimilarity. The clustering result suggests that simple dynamical mechanisms determine how countries respond to changes in COVID-19 case counts. Inspired by these results, we extend the simple SIR model for disease spread to include a social response to explain the number X(t) of new confirmed daily cases. In particular, we characterize the social response with a first-order model that depends on three parameters ν1,ν2,ν3. The parameter ν1 describes the effect of relaxed intervention when the incidence rate is low; ν2 models the impact of interventions when incidence rate is high; ν3 represents the fatigue, i.e., the weakening of interventions as time passes. The proposed model reproduces typical evolving patterns of COVID-19 epidemic waves observed in many countries. Estimating the parameters ν1,ν2,ν3 and initial conditions, such as R0, for different countries helps to identify important dynamics in their social responses. One conclusion is that the leading cause of the strong second wave in Europe in the fall of 2020 was not the relaxation of interventions during the summer, but rather the failure to enforce interventions in the fall.

For dengue fever and other seasonal epidemics we show how the stability of the preceding inter-outbreak period can predict subsequent total outbreak magnitude, and that a feasible stability metric can be computed from incidence data alone. As an observable of a dynamical system, incidence data contains information about the underlying mechanisms: climatic drivers, changing serotype pools, the ecology of the vector populations, and evolving viral strains. We present mathematical arguments to suggest a connection between stability measured in incidence data during the inter-outbreak period and the size of the effective susceptible population. The method is illustrated with an analysis of dengue incidence in San Juan, Puerto Rico, where forecasts can be made as early as three to four months ahead of an outbreak. These results have immediate significance for public health planning, and can be used in combination with existing forecasting methods and more comprehensive dengue models. Directly measuring the size of the susceptible population is usually unfeasible before dengue outbreaks. Here, the authors show that the stability of low-incidence periods provides a proxy measure, which can be estimated from incidence data, and show its utility for forecasting outbreaks.

To suppress the COVID-19 outbreak, the Norwegian government closed all schools on March 13, 2020. The kindergartens reopened on April 20, and the schools on April 27 and May 11 of 2020. The effect of these measures is largely unknown since the role of children in the spread of the SARS-CoV-2 virus is still unclear. There are only a few studies of school closures as a separate intervention to other social distancing measures, and little research exists on the effect of school opening during a pandemic. This study aimed to model the effect of opening kindergartens and the schools in Norway in terms of a change in the reproduction number (R). A secondary objective was to assess if we can use the estimated R after school openings to infer the rates of transmission between children in schools. We used an individual-based model (IBM) to assess the reopening of kindergartens and schools in two Norwegian cities, Oslo, the Norwegian capital, with a population of approximately 680 000, and Tromsø, which is the largest city in Northern Norway, with a population of approximately 75 000. The model uses demographic information and detailed data about the schools in both cities. We carried out an ensemble study to obtain robust results in spite of the considerable uncertainty that remains about the transmission of SARS-CoV-2. We found that reopening of Norwegian kindergartens and schools are associated with a change in R of 0.10 (95%CI 0.04-0.16) and 0.14 (95%CI 0.01-0.25) in the two cities under investigation if the in-school transmission rates for the SARS-CoV-2 virus are equal to what has previously been estimated for influenza pandemics. We found only a limited effect of reopening schools on the reproduction number, and we expect the same to hold true in other countries where nonpharmaceutical interventions have suppressed the pandemic. Consequently, current R-estimates are insufficiently accurate for determining the transmission rates in schools. For countries that have closed schools, planned interventions, such as the opening of selected schools, can be useful to infer general knowledge about children-to-children transmission of SARS-CoV-2.

The Greenland Ice Sheet (GrIS) is a potentially unstable component of the Earth system and may exhibit a critical transition under ongoing global warming. Mass reductions of the GrIS have substantial impacts on global sea level and the speed of the Atlantic Meridional Overturning Circulation, due to the additional freshwater caused by increased meltwater runoff into the northern Atlantic. The stability of the GrIS depends crucially on the positive melt-elevation feedback (MEF), by which melt rates increase as the overall ice sheet height decreases under rising temperatures. Melting rates across Greenland have accelerated nonlinearly in recent decades, and models predict a critical temperature threshold beyond which the current ice sheet state is not maintainable. Here, we investigate long-term melt rate and ice sheet height reconstructions from the central-western GrIS in combination with model simulations to quantify the stability of this part of the GrIS. We reveal significant early-warning signals (EWS) indicating that the central-western GrIS is close to a critical transition. By relating the statistical EWS to underlying physical processes, our results suggest that the MEF plays a dominant role in the observed, ongoing destabilization of the central-western GrIS. Our results suggest substantial further GrIS mass loss in the near future and call for urgent, observation-constrained stability assessments of other parts of the GrIS.

Kawasaki Disease (KD) is the most common cause of pediatric acquired heart disease, but its etiology remains unknown. We examined 1164 cases of KD treated at a regional children’s hospital in San Diego over a period of 15 years and uncovered novel structure to disease incidence. KD cases showed a well-defined seasonal variability, but also clustered temporally at much shorter time scales (days to weeks), and spatiotemporally on time scales of up to 10 days and spatial scales of 10–100 km. Temporal clusters of KD cases were associated with strongly significant regional-scale air temperature anomalies and consistent larger-scale atmospheric circulation patterns. Gene expression analysis further revealed a natural partitioning of KD patients into distinct groups based on their gene expression pattern, and that the different groups were associated with certain clinical characteristics that also exhibit temporal autocorrelation. Our data suggest that one or more environmental triggers exist, and that episodic exposures are modulated at least in part by regional weather conditions. We propose that characterization of the environmental factors that trigger KD in genetically susceptible children should focus on aerosols inhaled by patients who share common disease characteristics.

Background The aim was to develop prediction rules that may guide early treatment decisions based on baseline clinical predictors of long-term unfavorable outcome in juvenile idiopathic arthritis (JIA). Methods In the Nordic JIA cohort, we assessed baseline disease characteristics as predictors of the following outcomes 8 years after disease onset. Non-achievement of remission off medication according to the preliminary Wallace criteria, functional disability assessed by Childhood Health Assessment Questionnaire (CHAQ) and Physical Summary Score (PhS) of the Child Health Questionnaire, and articular damage assessed by the Juvenile Arthritis Damage Index-Articular (JADI-A). Multivariable models were constructed, and cross-validations were performed by repeated partitioning of the cohort into training sets for developing prediction models and validation sets to test predictive ability. Results The total cohort constituted 423 children. Remission status was available in 410 children: 244 (59.5%) of these did not achieve remission off medication at the final study visit. Functional disability was present in 111/340 (32.7%) children assessed by CHAQ and 40/199 (20.1%) by PhS, and joint damage was found in 29/216 (13.4%). Model performance was acceptable for making predictions of long-term outcome. In validation sets, the area under the curves (AUCs) in the receiver operating characteristic (ROC) curves were 0.78 (IQR 0.72–0.82) for non-achievement of remission off medication, 0.73 (IQR 0.67–0.76) for functional disability assessed by CHAQ, 0.74 (IQR 0.65–0.80) for functional disability assessed by PhS, and 0.73 (IQR 0.63–0.76) for joint damage using JADI-A. Conclusion The feasibility of making long-term predictions of JIA outcome based on early clinical assessment is demonstrated. The prediction models have acceptable precision and require only readily available baseline variables. Further testing in other cohorts is warranted.

The Arctic sea ice (ASI) is expected to decrease with further global warming. However, considerable uncertainty remains regarding the temperature range that would lead to a completely ice-free Arctic. Here, we combine satellite data and a large suite of models from the latest phase of the Coupled Model Intercomparison Project (CMIP6) to develop an empirical, observation-based projection of the September ASI area for increasing global mean surface temperature (GMST) values. This projection harnesses two simple linear relationships that are statistically supported by both observations and model data. First, we show that the September ASI area is linearly proportional to the area inside a specific northern hemisphere January–September mean temperature contour T c . Second, we use observational data to show how zonally averaged temperatures have followed a positive linear trend relative to the GMST, consistent with Arctic amplification. To ensure the reliability of these observations throughout the rest of the century, we validate this trend by employing the CMIP6 ensemble. Combining these two linear relationships, we show that the September ASI area decrease will accelerate with respect to the GMST increase. Our analysis of observations and CMIP6 model data suggests a complete loss of the September ASI (area below 10 6 km 2 ) for global warming between 1.5 ∘ C and 2.2 ∘ C above pre-industrial GMST levels.

The climate system approaches a tipping point if the prevailing climate state loses stability, making a transition to a different state possible. A result from the theory of randomly driven dynamical systems is that the reduced stability in the vicinity of a tipping point is accompanied by increasing fluctuation levels and longer correlation times (critical slowing down) and can in principle serve as early-warning signals of an upcoming tipping point. This study demonstrates that the high-frequency band of the δ 18O variations in the North Greenland Ice Core Project displays fluctuation levels that increase as one approaches the onset of an interstadial (warm) period. Similar results are found for the locally estimated Hurst exponent for the high-frequency fluctuations, signaling longer correlation times. The observed slowing down is found to be even stronger in the Younger Dryas, suggesting that both the Younger Dryas–Preboreal transition and the onsets of the Greenland interstadials are preceded by decreasing stability of the climate state. It is also verified that the temperature fluctuations during the stadial periods can be approximately modeled as a scale-invariant persistent noise, which can be approximated as an aggregation of processes that respond to perturbations on certain characteristic time scales. The results are consistent with the hypothesis that both the onsets of the Greenland interstadials and the Younger Dryas–Preboreal transition are caused by tipping points in dynamical processes with characteristic time scales on the order of decades and that the variability of other processes on longer time scales masks the early-warning signatures in the δ 18O signal.

Background Models to predict disease course and long-term outcome based on clinical characteristics at disease onset may guide early treatment strategies in juvenile idiopathic arthritis (JIA). Before a prediction model can be recommended for use in clinical practice, it needs to be validated in a different cohort than the one used for building the model. The aim of the current study was to validate the predictive performance of the Canadian prediction model developed by Guzman et al. and the Nordic model derived from Rypdal et al. to predict severe disease course and non-achievement of remission in Nordic patients with JIA. Methods The Canadian and Nordic multivariable logistic regression models were evaluated in the Nordic JIA cohort for prediction of non-achievement of remission, and the data-driven outcome denoted severe disease course. A total of 440 patients in the Nordic cohort with a baseline visit and an 8-year visit were included. The Canadian prediction model was first externally validated exactly as published. Both the Nordic and Canadian models were subsequently evaluated with repeated fine-tuning of model coefficients in training sets and testing in disjoint validation sets. The predictive performances of the models were assessed with receiver operating characteristic curves and C-indices. A model with a C-index above 0.7 was considered useful for clinical prediction. Results The Canadian prediction model had excellent predictive ability and was comparable in performance to the Nordic model in predicting severe disease course in the Nordic JIA cohort. The Canadian model yielded a C-index of 0.85 (IQR 0.83–0.87) for prediction of severe disease course and a C-index of 0.66 (0.63–0.68) for prediction of non-achievement of remission when applied directly. The median C-indices after fine-tuning were 0.85 (0.80–0.89) and 0.69 (0.65–0.73), respectively. Internal validation of the Nordic model for prediction of severe disease course resulted in a median C-index of 0.90 (0.86–0.92). Conclusions External validation of the Canadian model and internal validation of the Nordic model with severe disease course as outcome confirm their predictive abilities. Our findings suggest that predicting long-term remission is more challenging than predicting severe disease course.

A linearized energy-balance model for global temperature is formulated, featuring a scale-invariant long-range memory (LRM) response and stochastic forcing representing the influence on the ocean heat reservoir from atmospheric weather systems. The model is parameterized by an effective response strength, the stochastic forcing strength, and the memory exponent. The instrumental global surface temperature record and the deterministic component of the forcing are used to estimate these parameters by means of the maximum-likelihood method. The residual obtained by subtracting the deterministic solution from the observed record is analyzed as a noise process and shown to be consistent with a long-memory time series model and inconsistent with a short-memory model. By decomposing the forcing record in contributions from solar, volcanic, and anthropogenic activity one can estimate the contribution of each to twentieth-century global warming. The LRM model is applied with a reconstruction of the forcing for the last millennium to predict the large-scale features of Northern Hemisphere temperature reconstructions, and the analysis of the residual also clearly favors the LRM model on millennium time scale. The decomposition of the forcing shows that volcanic aerosols give a considerably greater contribution to the cooling during the Little Ice Age than the reduction in solar irradiance associated with the Maunder Minimum in solar activity. The LRM model implies a transient climate response in agreement with IPCC projections, but the stronger response on longer time scales suggests replacing the notion of equilibrium climate sensitivity by a time scale–dependent sensitivity.