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The Oberwolfach problem, posed by Ringel in 1967, asks for a decomposition of K2n+1 into edge-disjoint copies of a given 2-factor. We show that this can be achieved for all large n. We actually prove a significantly more general result, which allows for decompositions into more general types of factors. In particular, this also resolves the Hamilton-Waterloo problem for large n. [ABSTRACT FROM AUTHOR]

The local resilience of a graph G with respect to a property P measures how much one has to change G locally in order to destroy P. We prove 'resilience' versions of several classical results about Hamiltonicity for the graph models Gn;p and Gn;d. In the setting of random regular graphs, we prove a resilience version of Dirac's theorem. More precisely, we show that, whenever d is suficiently large compared to " > 0, a.a.s. the following holds. Let G0 be any subgraph of the random n-vertex d-regular graph Gn;d with minimum degree at least (1=2 +)d. Then G0 is Hamiltonian. This proves a conjecture of Ben-Shimon, Krivelevich and Sudakov. For the binomial random graph Gn;p, we prove a resilience version of Pósa's Hamiltonicity condition, and show that a natural guess for a resilience version of Chvsatal's theorem fails to be true. [ABSTRACT FROM AUTHOR]

Background: Seasonal influenza infects 5-20% of people every year in the United States, resulting in hospitalizations, deaths, and adverse economic impacts. To mitigate these impacts, influenza vaccines are developed and distributed annually; however, growing evidence suggests that vaccine effectiveness (VE) wanes over the course of a flu season. Delaying influenza vaccination for older adults has attracted attention as a potential public health strategy. However, given the uncertainties in seasonal peak, vaccine effectiveness, and waning rates, postponing vaccination could also lead to increased morbidity, motivating an evaluation of a range of potential scenarios., Methods: We systematically investigated a broad range of vaccination start times for five age groups under six combinations of initial effectiveness and waning rates, based on influenza cases and vaccine uptake data from 10 influenza seasons. We defined the most favorable vaccination schedule as the one that resulted in the greatest reduction in disease burden., Results: In scenarios with fast waning, all age groups benefit from delaying vaccination regardless of initial VE and peak timing. In scenarios with slower waning, results are mixed. For the ≥65 group, high initial VE and slow waning suggests that in early-peaking seasons, early vaccination most effectively reduces disease burden, while in late-peaking seasons delaying vaccination is most effective. For the ≥65 group in medium and low initial VE, and slow waning scenarios, delaying vaccination appears to prevent the greatest number of cases, regardless of whether the season peaks early or late., Conclusion: The most favorable vaccination schedule is sensitive to changes in initial VE, waning rate, and peak timing. Given estimates of these quantities from statistical and immunological models and observations, our methods can inform vaccination recommendations in order to most effectively reduce the annual disease burden caused by seasonal influenza. Specifically, accurate peak timing forecasts for the upcoming season have the potential to guide decisions on when to vaccinate., Competing Interests: Declarations Competing interests No competing interests are declared.

During the COVID-19 pandemic, forecasting COVID-19 trends to support planning and response was a priority for scientists and decision makers alike. In the United States, COVID-19 forecasting was coordinated by a large group of universities, companies, and government entities led by the Centers for Disease Control and Prevention and the US COVID-19 Forecast Hub (https://covid19forecasthub.org). We evaluated approximately 9.7 million forecasts of weekly state-level COVID-19 cases for predictions 1-4 weeks into the future submitted by 24 teams from August 2020 to December 2021. We assessed coverage of central prediction intervals and weighted interval scores (WIS), adjusting for missing forecasts relative to a baseline forecast, and used a Gaussian generalized estimating equation (GEE) model to evaluate differences in skill across epidemic phases that were defined by the effective reproduction number. Overall, we found high variation in skill across individual models, with ensemble-based forecasts outperforming other approaches. Forecast skill relative to the baseline was generally higher for larger jurisdictions (e.g., states compared to counties). Over time, forecasts generally performed worst in periods of rapid changes in reported cases (either in increasing or decreasing epidemic phases) with 95% prediction interval coverage dropping below 50% during the growth phases of the winter 2020, Delta, and Omicron waves. Ideally, case forecasts could serve as a leading indicator of changes in transmission dynamics. However, while most COVID-19 case forecasts outperformed a naïve baseline model, even the most accurate case forecasts were unreliable in key phases. Further research could improve forecasts of leading indicators, like COVID-19 cases, by leveraging additional real-time data, addressing performance across phases, improving the characterization of forecast confidence, and ensuring that forecasts were coherent across spatial scales. In the meantime, it is critical for forecast users to appreciate current limitations and use a broad set of indicators to inform pandemic-related decision making., Competing Interests: I have read the journal’s policy and the authors of this manuscript have the following competing interests: APP report grants from Metabiota Inc outside the submitted work. J.S. and Columbia University declare partial ownership of SK Analytics. No other authors have competing interests to declare., (Copyright: This is an open access article, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. The work is made available under the Creative Commons CC0 public domain dedication.)

Background: Short-term forecasts of infectious disease burden can contribute to situational awareness and aid capacity planning. Based on best practice in other fields and recent insights in infectious disease epidemiology, one can maximise the predictive performance of such forecasts if multiple models are combined into an ensemble. Here, we report on the performance of ensembles in predicting COVID-19 cases and deaths across Europe between 08 March 2021 and 07 March 2022., Methods: We used open-source tools to develop a public European COVID-19 Forecast Hub. We invited groups globally to contribute weekly forecasts for COVID-19 cases and deaths reported by a standardised source for 32 countries over the next 1-4 weeks. Teams submitted forecasts from March 2021 using standardised quantiles of the predictive distribution. Each week we created an ensemble forecast, where each predictive quantile was calculated as the equally-weighted average (initially the mean and then from 26th July the median) of all individual models' predictive quantiles. We measured the performance of each model using the relative Weighted Interval Score (WIS), comparing models' forecast accuracy relative to all other models. We retrospectively explored alternative methods for ensemble forecasts, including weighted averages based on models' past predictive performance., Results: Over 52 weeks, we collected forecasts from 48 unique models. We evaluated 29 models' forecast scores in comparison to the ensemble model. We found a weekly ensemble had a consistently strong performance across countries over time. Across all horizons and locations, the ensemble performed better on relative WIS than 83% of participating models' forecasts of incident cases (with a total N=886 predictions from 23 unique models), and 91% of participating models' forecasts of deaths (N=763 predictions from 20 models). Across a 1-4 week time horizon, ensemble performance declined with longer forecast periods when forecasting cases, but remained stable over 4 weeks for incident death forecasts. In every forecast across 32 countries, the ensemble outperformed most contributing models when forecasting either cases or deaths, frequently outperforming all of its individual component models. Among several choices of ensemble methods we found that the most influential and best choice was to use a median average of models instead of using the mean, regardless of methods of weighting component forecast models., Conclusions: Our results support the use of combining forecasts from individual models into an ensemble in order to improve predictive performance across epidemiological targets and populations during infectious disease epidemics. Our findings further suggest that median ensemble methods yield better predictive performance more than ones based on means. Our findings also highlight that forecast consumers should place more weight on incident death forecasts than incident case forecasts at forecast horizons greater than 2 weeks., Funding: AA, BH, BL, LWa, MMa, PP, SV funded by National Institutes of Health (NIH) Grant 1R01GM109718, NSF BIG DATA Grant IIS-1633028, NSF Grant No.: OAC-1916805, NSF Expeditions in Computing Grant CCF-1918656, CCF-1917819, NSF RAPID CNS-2028004, NSF RAPID OAC-2027541, US Centers for Disease Control and Prevention 75D30119C05935, a grant from Google, University of Virginia Strategic Investment Fund award number SIF160, Defense Threat Reduction Agency (DTRA) under Contract No. HDTRA1-19-D-0007, and respectively Virginia Dept of Health Grant VDH-21-501-0141, VDH-21-501-0143, VDH-21-501-0147, VDH-21-501-0145, VDH-21-501-0146, VDH-21-501-0142, VDH-21-501-0148. AF, AMa, GL funded by SMIGE - Modelli statistici inferenziali per governare l'epidemia, FISR 2020-Covid-19 I Fase, FISR2020IP-00156, Codice Progetto: PRJ-0695. AM, BK, FD, FR, JK, JN, JZ, KN, MG, MR, MS, RB funded by Ministry of Science and Higher Education of Poland with grant 28/WFSN/2021 to the University of Warsaw. BRe, CPe, JLAz funded by Ministerio de Sanidad/ISCIII. BT, PG funded by PERISCOPE European H2020 project, contract number 101016233. CP, DL, EA, MC, SA funded by European Commission - Directorate-General for Communications Networks, Content and Technology through the contract LC-01485746, and Ministerio de Ciencia, Innovacion y Universidades and FEDER, with the project PGC2018-095456-B-I00. DE., MGu funded by Spanish Ministry of Health / REACT-UE (FEDER). DO, GF, IMi, LC funded by Laboratory Directed Research and Development program of Los Alamos National Laboratory (LANL) under project number 20200700ER. DS, ELR, GG, NGR, NW, YW funded by National Institutes of General Medical Sciences (R35GM119582; the content is solely the responsibility of the authors and does not necessarily represent the official views of NIGMS or the National Institutes of Health). FB, FP funded by InPresa, Lombardy Region, Italy. HG, KS funded by European Centre for Disease Prevention and Control. IV funded by Agencia de Qualitat i Avaluacio Sanitaries de Catalunya (AQuAS) through contract 2021-021OE. JDe, SMo, VP funded by Netzwerk Universitatsmedizin (NUM) project egePan (01KX2021). JPB, SH, TH funded by Federal Ministry of Education and Research (BMBF; grant 05M18SIA). KH, MSc, YKh funded by Project SaxoCOV, funded by the German Free State of Saxony. Presentation of data, model results and simulations also funded by the NFDI4Health Task Force COVID-19 (https://www.nfdi4health.de/task-force-covid-19-2) within the framework of a DFG-project (LO-342/17-1). LP, VE funded by Mathematical and Statistical modelling project (MUNI/A/1615/2020), Online platform for real-time monitoring, analysis and management of epidemic situations (MUNI/11/02202001/2020); VE also supported by RECETOX research infrastructure (Ministry of Education, Youth and Sports of the Czech Republic: LM2018121), the CETOCOEN EXCELLENCE (CZ.02.1.01/0.0/0.0/17-043/0009632), RECETOX RI project (CZ.02.1.01/0.0/0.0/16-013/0001761). NIB funded by Health Protection Research Unit (grant code NIHR200908). SAb, SF funded by Wellcome Trust (210758/Z/18/Z)., Competing Interests: KS, HG, RG, HJ, RN, BP, FS, JD, DW, SA, AU, GG, ER, NR, DS, YW, NW, LW, JT, GO, TS, DT, LP, EK, JM, MB, NL, JM, JS, JW, JF, BL, IR, JB, RW, IV, VT, MS, MZ, CP, BR, NB, SM, LC, GF, IM, DO, PA, AM, VE, AK, DK, LP, BD, ML, SS, JD, SM, VP, GR, BB, GA, NP, GZ, WB, SH, TH, DS, MG, JA, DM, SA, EA, DL, CP, JB, AR, TZ, AK, JZ, FP, FD, MC, GL, PG, BT, FB, GJ, MM, AF, AS, PM, AA, BH, BL, MM, PP, SV, RB, FD, AG, KG, MG, BK, AM, KN, JN, MR, FR, MS, ES, JZ, JK, BP, KH, YK, MS, BP, MB, MF, RI, TK, TO, JB, SF No competing interests declared, PB, HG, SS, BS Affiliated with IEM, Inc. The author has no financial interests to declare

Background: West Nile virus (WNV) is the leading cause of mosquito-borne illness in the continental USA. WNV occurrence has high spatiotemporal variation, and current approaches to targeted control of the virus are limited, making forecasting a public health priority. However, little research has been done to compare strengths and weaknesses of WNV disease forecasting approaches on the national scale. We used forecasts submitted to the 2020 WNV Forecasting Challenge, an open challenge organized by the Centers for Disease Control and Prevention, to assess the status of WNV neuroinvasive disease (WNND) prediction and identify avenues for improvement., Methods: We performed a multi-model comparative assessment of probabilistic forecasts submitted by 15 teams for annual WNND cases in US counties for 2020 and assessed forecast accuracy, calibration, and discriminatory power. In the evaluation, we included forecasts produced by comparison models of varying complexity as benchmarks of forecast performance. We also used regression analysis to identify modeling approaches and contextual factors that were associated with forecast skill., Results: Simple models based on historical WNND cases generally scored better than more complex models and combined higher discriminatory power with better calibration of uncertainty. Forecast skill improved across updated forecast submissions submitted during the 2020 season. Among models using additional data, inclusion of climate or human demographic data was associated with higher skill, while inclusion of mosquito or land use data was associated with lower skill. We also identified population size, extreme minimum winter temperature, and interannual variation in WNND cases as county-level characteristics associated with variation in forecast skill., Conclusions: Historical WNND cases were strong predictors of future cases with minimal increase in skill achieved by models that included other factors. Although opportunities might exist to specifically improve predictions for areas with large populations and low or high winter temperatures, areas with high case-count variability are intrinsically more difficult to predict. Also, the prediction of outbreaks, which are outliers relative to typical case numbers, remains difficult. Further improvements to prediction could be obtained with improved calibration of forecast uncertainty and access to real-time data streams (e.g. current weather and preliminary human cases)., (© 2023. This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply.)

Infectious disease forecasting is of great interest to the public health community and policymakers, since forecasts can provide insight into disease dynamics in the near future and inform interventions. Due to delays in case reporting, however, forecasting models may often underestimate the current and future disease burden. In this paper, we propose a general framework for addressing reporting delay in disease forecasting efforts with the goal of improving forecasts. We propose strategies for leveraging either historical data on case reporting or external internet-based data to estimate the amount of reporting error. We then describe several approaches for adapting general forecasting pipelines to account for under- or over-reporting of cases. We apply these methods to address reporting delay in data on dengue fever cases in Puerto Rico from 1990 to 2009 and to reports of influenza-like illness (ILI) in the United States between 2010 and 2019. Through a simulation study, we compare method performance and evaluate robustness to assumption violations. Our results show that forecasting accuracy and prediction coverage almost always increase when correction methods are implemented to address reporting delay. Some of these methods required knowledge about the reporting error or high quality external data, which may not always be available. Provided alternatives include excluding recently-reported data and performing sensitivity analysis. This work provides intuition and guidance for handling delay in disease case reporting and may serve as a useful resource to inform practical infectious disease forecasting efforts., Competing Interests: The authors have declared that no competing interests exist.

Short-term probabilistic forecasts of the trajectory of the COVID-19 pandemic in the United States have served as a visible and important communication channel between the scientific modeling community and both the general public and decision-makers. Forecasting models provide specific, quantitative, and evaluable predictions that inform short-term decisions such as healthcare staffing needs, school closures, and allocation of medical supplies. Starting in April 2020, the US COVID-19 Forecast Hub (https://covid19forecasthub.org/) collected, disseminated, and synthesized tens of millions of specific predictions from more than 90 different academic, industry, and independent research groups. A multimodel ensemble forecast that combined predictions from dozens of groups every week provided the most consistently accurate probabilistic forecasts of incident deaths due to COVID-19 at the state and national level from April 2020 through October 2021. The performance of 27 individual models that submitted complete forecasts of COVID-19 deaths consistently throughout this year showed high variability in forecast skill across time, geospatial units, and forecast horizons. Two-thirds of the models evaluated showed better accuracy than a naïve baseline model. Forecast accuracy degraded as models made predictions further into the future, with probabilistic error at a 20-wk horizon three to five times larger than when predicting at a 1-wk horizon. This project underscores the role that collaboration and active coordination between governmental public-health agencies, academic modeling teams, and industry partners can play in developing modern modeling capabilities to support local, state, and federal response to outbreaks.

Infectious disease forecasting is an emerging field and has the potential to improve public health through anticipatory resource allocation, situational awareness, and mitigation planning. By way of exploring and operationalizing disease forecasting, the U.S. Centers for Disease Control and Prevention (CDC) has hosted FluSight since the 2013/14 flu season, an annual flu forecasting challenge. Since FluSight's onset, forecasters have developed and improved forecasting models in an effort to provide more timely, reliable, and accurate information about the likely progression of the outbreak. While improving the predictive performance of these forecasting models is often the primary objective, it is also important for a forecasting model to run quickly, facilitating further model development and improvement while providing flexibility when deployed in a real-time setting. In this vein I introduce Inferno, a fast and accurate flu forecasting model inspired by Dante, the top performing model in the 2018/19 FluSight challenge. When pseudoprospectively compared to all models that participated in FluSight 2018/19, Inferno would have placed 2nd in the national and regional challenge as well as the state challenge, behind only Dante. Inferno, however, runs in minutes and is trivially parallelizable, while Dante takes hours to run, representing a significant operational improvement with minimal impact to performance. Forecasting challenges like FluSight should continue to monitor and evaluate how they can be modified and expanded to incentivize the development of forecasting models that benefit public health., Competing Interests: The author has declared that no competing interests exist.

Background: Prior to the COVID-19 pandemic, US hospitals relied on static projections of future trends for long-term planning and were only beginning to consider forecasting methods for short-term planning of staffing and other resources. With the overwhelming burden imposed by COVID-19 on the health care system, an emergent need exists to accurately forecast hospitalization needs within an actionable timeframe., Objective: Our goal was to leverage an existing COVID-19 case and death forecasting tool to generate the expected number of concurrent hospitalizations, occupied intensive care unit (ICU) beds, and in-use ventilators 1 day to 4 weeks in the future for New Mexico and each of its five health regions., Methods: We developed a probabilistic model that took as input the number of new COVID-19 cases for New Mexico from Los Alamos National Laboratory's COVID-19 Forecasts Using Fast Evaluations and Estimation tool, and we used the model to estimate the number of new daily hospital admissions 4 weeks into the future based on current statewide hospitalization rates. The model estimated the number of new admissions that would require an ICU bed or use of a ventilator and then projected the individual lengths of hospital stays based on the resource need. By tracking the lengths of stay through time, we captured the projected simultaneous need for inpatient beds, ICU beds, and ventilators. We used a postprocessing method to adjust the forecasts based on the differences between prior forecasts and the subsequent observed data. Thus, we ensured that our forecasts could reflect a dynamically changing situation on the ground., Results: Forecasts made between September 1 and December 9, 2020, showed variable accuracy across time, health care resource needs, and forecast horizon. Forecasts made in October, when new COVID-19 cases were steadily increasing, had an average accuracy error of 20.0%, while the error in forecasts made in September, a month with low COVID-19 activity, was 39.7%. Across health care use categories, state-level forecasts were more accurate than those at the regional level. Although the accuracy declined as the forecast was projected further into the future, the stated uncertainty of the prediction improved. Forecasts were within 5% of their stated uncertainty at the 50% and 90% prediction intervals at the 3- to 4-week forecast horizon for state-level inpatient and ICU needs. However, uncertainty intervals were too narrow for forecasts of state-level ventilator need and all regional health care resource needs., Conclusions: Real-time forecasting of the burden imposed by a spreading infectious disease is a crucial component of decision support during a public health emergency. Our proposed methodology demonstrated utility in providing near-term forecasts, particularly at the state level. This tool can aid other stakeholders as they face COVID-19 population impacts now and in the future., (©Lauren A Castro, Courtney D Shelley, Dave Osthus, Isaac Michaud, Jason Mitchell, Carrie A Manore, Sara Y Del Valle. Originally published in JMIR Public Health and Surveillance (https://publichealth.jmir.org), 09.06.2021.)

Dengue virus remains a significant public health challenge in Brazil, and seasonal preparation efforts are hindered by variable intra- and interseasonal dynamics. Here, we present a framework for characterizing weekly dengue activity at the Brazilian mesoregion level from 2010-2016 as time series properties that are relevant to forecasting efforts, focusing on outbreak shape, seasonal timing, and pairwise correlations in magnitude and onset. In addition, we use a combination of 18 satellite remote sensing imagery, weather, clinical, mobility, and census data streams and regression methods to identify a parsimonious set of covariates that explain each time series property. The models explained 54% of the variation in outbreak shape, 38% of seasonal onset, 34% of pairwise correlation in outbreak timing, and 11% of pairwise correlation in outbreak magnitude. Regions that have experienced longer periods of drought sensitivity, as captured by the "normalized burn ratio," experienced less intense outbreaks, while regions with regular fluctuations in relative humidity had less regular seasonal outbreaks. Both the pairwise correlations in outbreak timing and outbreak trend between mesoresgions were best predicted by distance. Our analysis also revealed the presence of distinct geographic clusters where dengue properties tend to be spatially correlated. Forecasting models aimed at predicting the dynamics of dengue activity need to identify the most salient variables capable of contributing to accurate predictions. Our findings show that successful models may need to leverage distinct variables in different locations and be catered to a specific task, such as predicting outbreak magnitude or timing characteristics, to be useful. This advocates in favor of "adaptive models" rather than "one-size-fits-all" models. The results of this study can be applied to improving spatial hierarchical or target-focused forecasting models of dengue activity across Brazil., Competing Interests: I have read the journal’s policy and the authors of this manuscript have the following competing interests: A.P.y.P and A.V. report grants from Metabiota Inc.

Influenza forecasting in the United States (US) is complex and challenging due to spatial and temporal variability, nested geographic scales of interest, and heterogeneous surveillance participation. Here we present Dante, a multiscale influenza forecasting model that learns rather than prescribes spatial, temporal, and surveillance data structure and generates coherent forecasts across state, regional, and national scales. We retrospectively compare Dante's short-term and seasonal forecasts for previous flu seasons to the Dynamic Bayesian Model (DBM), a leading competitor. Dante outperformed DBM for nearly all spatial units, flu seasons, geographic scales, and forecasting targets. Dante's sharper and more accurate forecasts also suggest greater public health utility. Dante placed 1st in the Centers for Disease Control and Prevention's prospective 2018/19 FluSight challenge in both the national and regional competition and the state competition. The methodology underpinning Dante can be used in other seasonal disease forecasting contexts having nested geographic scales of interest.

With an estimated $10.4 billion in medical costs and 31.4 million outpatient visits each year, influenza poses a serious burden of disease in the United States. To provide insights and advance warning into the spread of influenza, the U.S. Centers for Disease Control and Prevention (CDC) runs a challenge for forecasting weighted influenza-like illness (wILI) at the national and regional level. Many models produce independent forecasts for each geographical unit, ignoring the constraint that the national wILI is a weighted sum of regional wILI, where the weights correspond to the population size of the region. We propose a novel algorithm that transforms a set of independent forecast distributions to obey this constraint, which we refer to as probabilistically coherent. Enforcing probabilistic coherence led to an increase in forecast skill for 79% of the models we tested over multiple flu seasons, highlighting the importance of respecting the forecasting system's geographical hierarchy., Competing Interests: The authors have declared that no competing interests exist.

Background: Dengue fever is a mosquito-borne infection transmitted by Aedes aegypti and mainly found in tropical and subtropical regions worldwide. Since its re-introduction in 1986, Brazil has become a hotspot for dengue and has experienced yearly epidemics. As a notifiable infectious disease, Brazil uses a passive epidemiological surveillance system to collect and report cases; however, dengue burden is underestimated. Thus, Internet data streams may complement surveillance activities by providing real-time information in the face of reporting lags., Methods: We analyzed 19 terms related to dengue using Google Health Trends (GHT), a free-Internet data-source, and compared it with weekly dengue incidence between 2011 to 2016. We correlated GHT data with dengue incidence at the national and state-level for Brazil while using the adjusted R squared statistic as primary outcome measure (0/1). We used survey data on Internet access and variables from the official census of 2010 to identify where GHT could be useful in tracking dengue dynamics. Finally, we used a standardized volatility index on dengue incidence and developed models with different variables with the same objective., Results: From the 19 terms explored with GHT, only seven were able to consistently track dengue. From the 27 states, only 12 reported an adjusted R squared higher than 0.8; these states were distributed mainly in the Northeast, Southeast, and South of Brazil. The usefulness of GHT was explained by the logarithm of the number of Internet users in the last 3 months, the total population per state, and the standardized volatility index., Conclusions: The potential contribution of GHT in complementing traditional established surveillance strategies should be analyzed in the context of geographical resolutions smaller than countries. For Brazil, GHT implementation should be analyzed in a case-by-case basis. State variables including total population, Internet usage in the last 3 months, and the standardized volatility index could serve as indicators determining when GHT could complement dengue state level surveillance in other countries.

Seasonal influenza results in substantial annual morbidity and mortality in the United States and worldwide. Accurate forecasts of key features of influenza epidemics, such as the timing and severity of the peak incidence in a given season, can inform public health response to outbreaks. As part of ongoing efforts to incorporate data and advanced analytical methods into public health decision-making, the United States Centers for Disease Control and Prevention (CDC) has organized seasonal influenza forecasting challenges since the 2013/2014 season. In the 2017/2018 season, 22 teams participated. A subset of four teams created a research consortium called the FluSight Network in early 2017. During the 2017/2018 season they worked together to produce a collaborative multi-model ensemble that combined 21 separate component models into a single model using a machine learning technique called stacking. This approach creates a weighted average of predictive densities where the weight for each component is determined by maximizing overall ensemble accuracy over past seasons. In the 2017/2018 influenza season, one of the largest seasonal outbreaks in the last 15 years, this multi-model ensemble performed better on average than all individual component models and placed second overall in the CDC challenge. It also outperformed the baseline multi-model ensemble created by the CDC that took a simple average of all models submitted to the forecasting challenge. This project shows that collaborative efforts between research teams to develop ensemble forecasting approaches can bring measurable improvements in forecast accuracy and important reductions in the variability of performance from year to year. Efforts such as this, that emphasize real-time testing and evaluation of forecasting models and facilitate the close collaboration between public health officials and modeling researchers, are essential to improving our understanding of how best to use forecasts to improve public health response to seasonal and emerging epidemic threats., Competing Interests: I have read the journal’s policy and the authors of this manuscript have the following competing interests: JS and Columbia University disclose partial ownership of SK Analytics.

Seasonal influenza is a sometimes surprisingly impactful disease, causing thousands of deaths per year along with much additional morbidity. Timely knowledge of the outbreak state is valuable for managing an effective response. The current state of the art is to gather this knowledge using in-person patient contact. While accurate, this is time-consuming and expensive. This has motivated inquiry into new approaches using internet activity traces, based on the theory that lay observations of health status lead to informative features in internet data. These approaches risk being deceived by activity traces having a coincidental, rather than informative, relationship to disease incidence; to our knowledge, this risk has not yet been quantitatively explored. We evaluated both simulated and real activity traces of varying deceptiveness for influenza incidence estimation using linear regression. We found that deceptiveness knowledge does reduce error in such estimates, that it may help automatically-selected features perform as well or better than features that require human curation, and that a semantic distance measure derived from the Wikipedia article category tree serves as a useful proxy for deceptiveness. This suggests that disease incidence estimation models should incorporate not only data about how internet features map to incidence but also additional data to estimate feature deceptiveness. By doing so, we may gain one more step along the path to accurate, reliable disease incidence estimation using internet data. This capability would improve public health by decreasing the cost and increasing the timeliness of such estimates., Competing Interests: The authors have declared that no competing interests exist.

Influenza infects an estimated 9-35 million individuals each year in the United States and is a contributing cause for between 12,000 and 56,000 deaths annually. Seasonal outbreaks of influenza are common in temperate regions of the world, with highest incidence typically occurring in colder and drier months of the year. Real-time forecasts of influenza transmission can inform public health response to outbreaks. We present the results of a multiinstitution collaborative effort to standardize the collection and evaluation of forecasting models for influenza in the United States for the 2010/2011 through 2016/2017 influenza seasons. For these seven seasons, we assembled weekly real-time forecasts of seven targets of public health interest from 22 different models. We compared forecast accuracy of each model relative to a historical baseline seasonal average. Across all regions of the United States, over half of the models showed consistently better performance than the historical baseline when forecasting incidence of influenza-like illness 1 wk, 2 wk, and 3 wk ahead of available data and when forecasting the timing and magnitude of the seasonal peak. In some regions, delays in data reporting were strongly and negatively associated with forecast accuracy. More timely reporting and an improved overall accessibility to novel and traditional data sources are needed to improve forecasting accuracy and its integration with real-time public health decision making., Competing Interests: Conflict of interest statement: J.S. and Columbia University disclose partial ownership of SK Analytics., (Copyright © 2019 the Author(s). Published by PNAS.)

The ability to produce timely and accurate flu forecasts in the United States can significantly impact public health. Augmenting forecasts with internet data has shown promise for improving forecast accuracy and timeliness in controlled settings, but results in practice are less convincing, as models augmented with internet data have not consistently outperformed models without internet data. In this paper, we perform a controlled experiment, taking into account data backfill, to improve clarity on the benefits and limitations of augmenting an already good flu forecasting model with internet-based nowcasts. Our results show that a good flu forecasting model can benefit from the augmentation of internet-based nowcasts in practice for all considered public health-relevant forecasting targets. The degree of forecast improvement due to nowcasting, however, is uneven across forecasting targets, with short-term forecasting targets seeing the largest improvements and seasonal targets such as the peak timing and intensity seeing relatively marginal improvements. The uneven forecasting improvements across targets hold even when "perfect" nowcasts are used. These findings suggest that further improvements to flu forecasting, particularly seasonal targets, will need to derive from other, non-nowcasting approaches., Competing Interests: The authors have declared that no competing interests exist.

Seasonal influenza is a serious public health and societal problem due to its consequences resulting from absenteeism, hospitalizations, and deaths. The overall burden of influenza is captured by the Centers for Disease Control and Prevention's influenza-like illness network, which provides invaluable information about the current incidence. This information is used to provide decision support regarding prevention and response efforts. Despite the relatively rich surveillance data and the recurrent nature of seasonal influenza, forecasting the timing and intensity of seasonal influenza in the U.S. remains challenging because the form of the disease transmission process is uncertain, the disease dynamics are only partially observed, and the public health observations are noisy. Fitting a probabilistic state-space model motivated by a deterministic mathematical model [a susceptible-infectious-recovered (SIR) model] is a promising approach for forecasting seasonal influenza while simultaneously accounting for multiple sources of uncertainty. A significant finding of this work is the importance of thoughtfully specifying the prior, as results critically depend on its specification. Our conditionally specified prior allows us to exploit known relationships between latent SIR initial conditions and parameters and functions of surveillance data. We demonstrate advantages of our approach relative to alternatives via a forecasting comparison using several forecast accuracy metrics.

Effective disease monitoring provides a foundation for effective public health systems. This has historically been accomplished with patient contact and bureaucratic aggregation, which tends to be slow and expensive. Recent internet-based approaches promise to be real-time and cheap, with few parameters. However, the question of when and how these approaches work remains open. We addressed this question using Wikipedia access logs and category links. Our experiments, replicable and extensible using our open source code and data, test the effect of semantic article filtering, amount of training data, forecast horizon, and model staleness by comparing across 6 diseases and 4 countries using thousands of individual models. We found that our minimal-configuration, language-agnostic article selection process based on semantic relatedness is effective for improving predictions, and that our approach is relatively insensitive to the amount and age of training data. We also found, in contrast to prior work, very little forecasting value, and we argue that this is consistent with theoretical considerations about the nature of forecasting. These mixed results lead us to propose that the currently observational field of internet-based disease surveillance must pivot to include theoretical models of information flow as well as controlled experiments based on simulations of disease.

Mathematical models, such as those that forecast the spread of epidemics or predict the weather, must overcome the challenges of integrating incomplete and inaccurate data in computer simulations, estimating the probability of multiple possible scenarios, incorporating changes in human behavior and/or the pathogen, and environmental factors. In the past 3 decades, the weather forecasting community has made significant advances in data collection, assimilating heterogeneous data steams into models and communicating the uncertainty of their predictions to the general public. Epidemic modelers are struggling with these same issues in forecasting the spread of emerging diseases, such as Zika virus infection and Ebola virus disease. While weather models rely on physical systems, data from satellites, and weather stations, epidemic models rely on human interactions, multiple data sources such as clinical surveillance and Internet data, and environmental or biological factors that can change the pathogen dynamics. We describe some of similarities and differences between these 2 fields and how the epidemic modeling community is rising to the challenges posed by forecasting to help anticipate and guide the mitigation of epidemics. We conclude that some of the fundamental differences between these 2 fields, such as human behavior, make disease forecasting more challenging than weather forecasting., (Published by Oxford University Press for the Infectious Diseases Society of America 2016. This work is written by (a) US Government employee(s) and is in the public domain in the US.)