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Background Ensemble modeling aims to boost the forecasting performance by systematically integrating the predictive accuracy across individual models. Here we introduce a simple-yet-powerful ensemble methodology for forecasting the trajectory of dynamic growth processes that are defined by a system of non-linear differential equations with applications to infectious disease spread. Methods We propose and assess the performance of two ensemble modeling schemes with different parametric bootstrapping procedures for trajectory forecasting and uncertainty quantification. Specifically, we conduct sequential probabilistic forecasts to evaluate their forecasting performance using simple dynamical growth models with good track records including the Richards model, the generalized-logistic growth model, and the Gompertz model. We first test and verify the functionality of the method using simulated data from phenomenological models and a mechanistic transmission model. Next, the performance of the method is demonstrated using a diversity of epidemic datasets including scenario outbreak data of the Ebola Forecasting Challenge and real-world epidemic data outbreaks of including influenza, plague, Zika, and COVID-19. Results We found that the ensemble method that randomly selects a model from the set of individual models for each time point of the trajectory of the epidemic frequently outcompeted the individual models as well as an alternative ensemble method based on the weighted combination of the individual models and yields broader and more realistic uncertainty bounds for the trajectory envelope, achieving not only better coverage rate of the 95% prediction interval but also improved mean interval scores across a diversity of epidemic datasets. Conclusion Our new methodology for ensemble forecasting outcompete component models and an alternative ensemble model that differ in how the variance is evaluated for the generation of the prediction intervals of the forecasts.

Many disciplines, such as public health, rely on statistical time series models for real-time and retrospective forecasting efforts; however, effectively implementing related methods often requires extensive programming knowledge. Therefore, such tools remain largely inaccessible to those with limited programming experience, including students training in modeling, as well as professionals and policymakers seeking to forecast an epidemic's trajectory. To address the need for accessible and intuitive forecasting applications, we present StatModPredict, an R-Shiny dashboard for conducting robust forecasting analysis utilizing auto-regressive integrated moving average (ARIMA), generalized linear models (GLM), generalized additive models (GAM), and Meta's Prophet model. StatModPredict supports robust real-time forecasting and retrospective model analysis, including fitting, forecasting, evaluation, visualization, and comparison of results from four popular models. After loading an incident time series data set into the interface, users can easily customize model parameters and forecasting options to obtain the desired output. Additionally, StatModPredict offers multiple editable figures for, but not limited to, the time series data, the forecasts, and model fit and forecast metrics. Users can also upload external forecasts produced elsewhere and evaluate their performance alongside the dashboard's built-in models, thereby enabling direct comparisons. We provide a detailed demonstration of the dashboard's features using publicly available annual HIV case data in the US. A video tutorial is available at https://www.youtube.com/watch?v=zgZOvqhvqw8. By eliminating programming barriers, StatModPredict facilitates exploration and use by students training in forecasting, as well as professionals and policymakers aiming to forecast epidemic trajectories. Additionally, the flexibility in the required input data structure and parameter specification process extends the application of StatModPredict to any discipline that employs time series data. By offering this open-source interface, we aim to broaden access to forecasting tools, promote hands-on learning, and foster contributions from users across disciplines.

Background Mathematical models based on ordinary differential equations (ODEs) are essential tools across various scientific disciplines, including biology, ecology, epidemic modeling, and healthcare informatics, where they are used to simulate complex dynamic systems and inform decision-making. However, implementing Bayesian calibration and forecasting typically requires substantial coding in Stan or similar tools. To support Bayesian parameter estimation and forecasting for such systems, we introduce BayesianFitForecast , a user-friendly R toolbox specifically developed to streamline Bayesian parameter estimation and forecasting in ODE models, making it particularly relevant to health informatics and public health decision-making ( https://github.com/gchowell/BayesianFitForecast/ ). Results This toolbox enables automatic generation of Stan files, allowing users to configure models, define priors, and analyze results with minimal programming expertise. By eliminating manual coding, BayesianFitForecast significantly lowers the technical barrier to Bayesian inference with dynamical systems. We demonstrate its flexibility and usability through applications to historical epidemic datasets (e.g., the 1918 influenza pandemic in San Francisco and the 1896–1897 Bombay plague) and simulated data, showing robust parameter estimation and forecasting performance under Poisson and negative binomial observation error structures. The toolbox also provides robust tools for evaluating model performance, including convergence diagnostics, posterior distributions, credible intervals, and performance metrics. Conclusion By improving the accessibility of advanced Bayesian methods, BayesianFitForecast broadens the application of Bayesian inference in time-series modeling, healthcare forecasting, and epidemiological applications. In addition to the R scripting interface, a built-in Shiny web application is included, enabling interactive model configuration, visualization, and forecasting. A tutorial video demonstrating the toolbox’s functionality is also available ( https://youtu.be/jnxMjz3V3n8 ).

The ongoing COVID-19 epidemic continues to spread within and outside of China, despite several social distancing measures implemented by the Chinese government. Limited epidemiological data are available, and recent changes in case definition and reporting further complicate our understanding of the impact of the epidemic, particularly in the epidemic’s epicenter. Here we use previously validated phenomenological models to generate short-term forecasts of cumulative reported cases in Guangdong and Zhejiang, China. Using daily reported cumulative case data up until 13 February 2020 from the National Health Commission of China, we report 5- and 10-day ahead forecasts of cumulative case reports. Specifically, we generate forecasts using a generalized logistic growth model, the Richards growth model, and a sub-epidemic wave model, which have each been previously used to forecast outbreaks due to different infectious diseases. Forecasts from each of the models suggest the outbreaks may be nearing extinction in both Guangdong and Zhejiang; however, the sub-epidemic model predictions also include the potential for further sustained transmission, particularly in Zhejiang. Our 10-day forecasts across the three models predict an additional 65–81 cases (upper bounds: 169–507) in Guangdong and an additional 44–354 (upper bounds: 141–875) cases in Zhejiang by February 23, 2020. In the best-case scenario, current data suggest that transmission in both provinces is slowing down.

Background Beginning May 7, 2022, multiple nations reported an unprecedented surge in monkeypox cases. Unlike past outbreaks, differences in affected populations, transmission mode, and clinical characteristics have been noted. With the existing uncertainties of the outbreak, real-time short-term forecasting can guide and evaluate the effectiveness of public health measures. Methods We obtained publicly available data on confirmed weekly cases of monkeypox at the global level and for seven countries (with the highest burden of disease at the time this study was initiated) from the Our World in Data (OWID) GitHub repository and CDC website. We generated short-term forecasts of new cases of monkeypox across the study areas using an ensemble n-sub-epidemic modeling framework based on weekly cases using 10-week calibration periods. We report and assess the weekly forecasts with quantified uncertainty from the top-ranked, second-ranked, and ensemble sub-epidemic models. Overall, we conducted 324 weekly sequential 4-week ahead forecasts across the models from the week of July 28th, 2022, to the week of October 13th, 2022. Results The last 10 of 12 forecasting periods (starting the week of August 11th, 2022) show either a plateauing or declining trend of monkeypox cases for all models and areas of study. According to our latest 4-week ahead forecast from the top-ranked model, a total of 6232 (95% PI 487.8, 12,468.0) cases could be added globally from the week of 10/20/2022 to the week of 11/10/2022. At the country level, the top-ranked model predicts that the USA will report the highest cumulative number of new cases for the 4-week forecasts (median based on OWID data: 1806 (95% PI 0.0, 5544.5)). The top-ranked and weighted ensemble models outperformed all other models in short-term forecasts. Conclusions Our top-ranked model consistently predicted a decreasing trend in monkeypox cases on the global and country-specific scale during the last ten sequential forecasting periods. Our findings reflect the potential impact of increased immunity, and behavioral modification among high-risk populations.

Since the detection of the first case of COVID-19 in Chile on March 3 rd , 2020, a total of 513,188 cases, including ~14,302 deaths have been reported in Chile as of November 2 nd , 2020. Here, we estimate the reproduction number throughout the epidemic in Chile and study the effectiveness of control interventions especially the effectiveness of lockdowns by conducting short-term forecasts based on the early transmission dynamics of COVID-19. Chile’s incidence curve displays early sub-exponential growth dynamics with the deceleration of growth parameter, p , estimated at 0.8 (95% CI: 0.7, 0.8) and the reproduction number, R , estimated at 1.8 (95% CI: 1.6, 1.9). Our findings indicate that the control measures at the start of the epidemic significantly slowed down the spread of the virus. However, the relaxation of restrictions and spread of the virus in low-income neighborhoods in May led to a new surge of infections, followed by the reimposition of lockdowns in Greater Santiago and other municipalities. These measures have decelerated the virus spread with R estimated at ~0.96 (95% CI: 0.95, 0.98) as of November 2 nd , 2020. The early sub-exponential growth trend ( p ~0.8) of the COVID-19 epidemic transformed into a linear growth trend ( p ~0.5) as of July 7 th , 2020, after the reimposition of lockdowns. While the broad scale social distancing interventions have slowed the virus spread, the number of new COVID-19 cases continue to accrue, underscoring the need for persistent social distancing and active case detection and isolation efforts to maintain the epidemic under control.

During the 2022–2023 unprecedented mpox epidemic, near real-time short-term forecasts of the epidemic’s trajectory were essential in intervention implementation and guiding policy. However, as case levels have significantly decreased, evaluating model performance is vital to advancing the field of epidemic forecasting. Using laboratory-confirmed mpox case data from the Centers for Disease Control and Prevention and Our World in Data teams, we generated retrospective sequential weekly forecasts for Brazil, Canada, France, Germany, Spain, the United Kingdom, the United States and at the global scale using an auto-regressive integrated moving average (ARIMA) model, generalized additive model, simple linear regression, Facebook’s Prophet model, as well as the sub-epidemic wave and n -sub-epidemic modelling frameworks. We assessed forecast performance using average mean squared error, mean absolute error, weighted interval scores, 95% prediction interval coverage, skill scores and Winkler scores. Overall, the n -sub-epidemic modelling framework outcompeted other models across most locations and forecasting horizons, with the unweighted ensemble model performing best most frequently. The n -sub-epidemic and spatial-wave frameworks considerably improved in average forecasting performance relative to the ARIMA model (greater than 10%) for all performance metrics. Findings further support sub-epidemic frameworks for short-term forecasting epidemics of emerging and re-emerging infectious diseases.

We analyze an ensemble of n -sub-epidemic modeling for forecasting the trajectory of epidemics and pandemics. These ensemble modeling approaches, and models that integrate sub-epidemics to capture complex temporal dynamics, have demonstrated powerful forecasting capability. This modeling framework can characterize complex epidemic patterns, including plateaus, epidemic resurgences, and epidemic waves characterized by multiple peaks of different sizes. We systematically assess their calibration and short-term forecasting performance in short-term forecasts for the COVID-19 pandemic in the USA from late April 2020 to late February 2022. We compare their performance with two commonly used statistical ARIMA models. The best fit sub-epidemic model and three ensemble models constructed using the top-ranking sub-epidemic models consistently outperformed the ARIMA models in terms of the weighted interval score (WIS) and the coverage of the 95% prediction interval across the 10-, 20-, and 30-day short-term forecasts. In our 30-day forecasts, the average WIS ranged from 377.6 to 421.3 for the sub-epidemic models, whereas it ranged from 439.29 to 767.05 for the ARIMA models. Across 98 short-term forecasts, the ensemble model incorporating the top four ranking sub-epidemic models (Ensemble(4)) outperformed the (log) ARIMA model 66.3% of the time, and the ARIMA model, 69.4% of the time in 30-day ahead forecasts in terms of the WIS. Ensemble(4) consistently yielded the best performance in terms of the metrics that account for the uncertainty of the predictions. This framework can be readily applied to investigate the spread of epidemics and pandemics beyond COVID-19, as well as other dynamic growth processes found in nature and society that would benefit from short-term predictions.

Simple dynamic modeling tools can help generate real-time short-term forecasts with quantified uncertainty of the trajectory of diverse growth processes unfolding in nature and society, including disease outbreaks. An easy-to-use and flexible toolbox for this purpose is lacking. This tutorial-based primer introduces and illustrates GrowthPredict , a user-friendly MATLAB toolbox for fitting and forecasting time-series trajectories using phenomenological dynamic growth models based on ordinary differential equations. This toolbox is accessible to a broad audience, including students training in mathematical biology, applied statistics, and infectious disease modeling, as well as researchers and policymakers who need to conduct short-term forecasts in real-time. The models included in the toolbox capture exponential and sub-exponential growth patterns that typically follow a rising pattern followed by a decline phase, a common feature of contagion processes. Models include the 1-parameter exponential growth model and the 2-parameter generalized-growth model, which have proven useful in characterizing and forecasting the ascending phase of epidemic outbreaks. It also includes the 2-parameter Gompertz model, the 3-parameter generalized logistic-growth model, and the 3-parameter Richards model, which have demonstrated competitive performance in forecasting single peak outbreaks. We provide detailed guidance on forecasting time-series trajectories and available software ( https://github.com/gchowell/forecasting_growthmodels ), including the full uncertainty distribution derived through parametric bootstrapping, which is needed to construct prediction intervals and evaluate their accuracy. Functions are available to assess forecasting performance across different models, estimation methods, error structures in the data, and forecasting horizons. The toolbox also includes functions to quantify forecasting performance using metrics that evaluate point and distributional forecasts, including the weighted interval score. This tutorial and toolbox can be broadly applied to characterizing and forecasting time-series data using simple phenomenological growth models. As a contagion process takes off, the tools presented in this tutorial can help create forecasts to guide policy regarding implementing control strategies and assess the impact of interventions. The toolbox functionality is demonstrated through various examples, including a tutorial video, and the examples use publicly available data on the monkeypox (mpox) epidemic in the USA.

The use of Electronic Nicotine Delivery Systems (ENDS), or vaping devices, has raised concerns about their potential impact on oral health, particularly periodontal disease. While traditional smoking is a well-established risk factor for periodontal disease, the biological and microbial effects of ENDS use are less well understood. Our study examined how vaping and vaping behaviors influence the subgingival plaque microbiome and the associated metabolic pathways that may contribute to oral disease. We enrolled 70 healthy adults aged 18–35, including 48 regular ENDS users and 22 non-vaping controls. ENDS users were categorized by puffing behavior into low, medium, and high flow groups using a validated topography device. All participants underwent periodontal screening and provided saliva and subgingival plaque samples. To evaluate exposure profiles, ENDS users also submitted their personal devices for emissions testing, and volatile organic compounds (VOCs) were collected and analyzed using gas chromatography-mass spectrometry and high-performance liquid chromatography. Compared to non-vapers, ENDS users demonstrated distinct shifts in their oral microbiome, with reductions in beneficial taxa and increased bacteria associated with inflammation and periodontal disease. These changes were more pronounced in high-puff volume users, who also exhibited lower microbial diversity. Functional profiling revealed vaping-associated enrichment of pathways related to lipid metabolism, inflammation, and xenobiotic degradation. Untargeted salivary metabolomics identified metabolic disruptions consistent with these functional shifts. Integrative network analyses incorporating VOC measurements demonstrated correlations between microbial composition, puff volume, and metabolic disruptions, particularly in lipid-regulated and inflammatory pathways. To our knowledge, this is one of the first studies to integrate vaping behavior, oral microbiome profiling, salivary metabolomics, and VOC emissions analysis in a human cohort. These findings suggest ENDS use, especially at higher intensities, may disrupt oral microbial and metabolic homeostasis through both biological and chemical pathways potentially enhancing periodontal disease risk. These patterns point to potential biological and chemical pathways of concern, warranting further investigation and informing public health priorities.