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
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Abstract 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.Free, publicly-accessible full text available December 1, 2025 -
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Abstract Background Dynamical mathematical models defined by a system of differential equations are typically not easily accessible to non-experts. However, forecasts based on these types of models can help gain insights into the mechanisms driving the process and may outcompete simpler phenomenological growth models. Here we introduce a friendly toolbox,
SpatialWavePredict , to characterize and forecast the spatial wave sub-epidemic model, which captures diverse wave dynamics by aggregating multiple asynchronous growth processes and has outperformed simpler phenomenological growth models in short-term forecasts of various infectious diseases outbreaks including SARS, Ebola, and the early waves of the COVID-19 pandemic in the US.Results This tutorial-based primer introduces and illustrates a user-friendly MATLAB toolbox for fitting and forecasting time-series trajectories using an ensemble spatial wave sub-epidemic model based on ordinary differential equations. Scientists, policymakers, and students can use the toolbox to conduct real-time short-term forecasts. The five-parameter epidemic wave model in the toolbox aggregates linked overlapping sub-epidemics and captures a rich spectrum of epidemic wave dynamics, including oscillatory wave behavior and plateaus. An ensemble strategy aims to improve forecasting performance by combining the resulting top-ranked models. The toolbox provides a tutorial for forecasting time-series trajectories, 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, 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.
Conclusions We have developed the first comprehensive toolbox to characterize and forecast time-series data using an ensemble spatial wave sub-epidemic wave model. As an epidemic situation or contagion occurs, the tools presented in this tutorial can facilitate policymakers to guide the implementation of containment strategies and assess the impact of control interventions. We demonstrate the functionality of the toolbox with examples, including a tutorial video, and is illustrated using daily data on the COVID-19 pandemic in the USA.
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Free, publicly-accessible full text available June 1, 2025
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Acharya, Binod (Ed.)This study compares pandemic experiences of Missouri’s 115 counties based on rurality and sociodemographic characteristics during the 1918–20 influenza and 2020–21 COVID-19 pandemics. The state’s counties and overall population distribution have remained relatively stable over the last century, which enables identification of long-lasting pandemic attributes. Sociodemographic data available at the county level for both time periods were taken from U.S. census data and used to create clusters of similar counties. Counties were also grouped by rural status (RSU), including fully (100%) rural, semirural (1–49% living in urban areas), and urban (>50% of the population living in urban areas). Deaths from 1918 through 1920 were collated from the Missouri Digital Heritage database and COVID-19 cases and deaths were downloaded from the Missouri COVID-19 dashboard. Results from sociodemographic analyses indicate that, during both time periods, average farm value, proportion White, and literacy were the most important determinants of sociodemographic clusters. Furthermore, the Urban/Central and Southeastern regions experienced higher mortality during both pandemics than did the North and South. Analyses comparing county groups by rurality indicated that throughout the 1918–20 influenza pandemic, urban counties had the highest and rural had the lowest mortality rates. Early in the 2020–21 COVID-19 pandemic, urban counties saw the most extensive epidemic spread and highest mortality, but as the epidemic progressed, cumulative mortality became highest in semirural counties. Additional results highlight the greater effects both pandemics had on county groups with lower rates of education and a lower proportion of Whites in the population. This was especially true for the far southeastern counties of Missouri (“the Bootheel”) during the COVID-19 pandemic. These results indicate that rural-urban and socioeconomic differences in health outcomes are long-standing problems that continue to be of significant importance, even though the overall quality of health care is substantially better in the 21 st century.more » « less
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Abstract 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.
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Introduction: The incidence of diarrhea, a leading cause of morbidity and mortality in low-income countries such as Nepal, is temperature-sensitive, suggesting it could be associated with climate change. With climate change fueled increases in the mean and variability of temperature and precipitation, the incidence of water and food-borne diseases are increasing, particularly in sub-Saharan Africa and South Asia. This national-level ecological study was undertaken to provide evidence linking weather and climate with diarrhea incidence in Nepal. Method: We analyzed monthly diarrheal disease count and meteorological data from all districts, spanning 15 eco-development regions of Nepal. Meteorological data and monthly data on diarrheal disease were sourced, respectively, from the Department of Hydrology and Meteorology and Health Management Information System (HMIS) of the Government of Nepal for the period from 2002 to 2014. Time-series log-linear regression models assessed the relationship between maximum temperature, minimum temperature, rainfall, relative humidity, and diarrhea burden. Predictors with p-values < 0.25 were retained in the fitted models. Results: Overall, diarrheal disease incidence in Nepal significantly increased with 1 °C increase in mean temperature (4.4%; 95% CI: 3.95, 4.85) and 1 cm increase in rainfall (0.28%; 95% CI: 0.15, 0.41). Seasonal variation of diarrheal incidence was prominent at the national level (11.63% rise in diarrheal cases in summer (95% CI: 4.17, 19.61) and 14.5% decrease in spring (95% CI: −18.81, −10.02) compared to winter season). Moreover, the effects of temperature and rainfall were highest in the mountain region compared to other ecological regions of Nepal. Conclusion: Our study provides empirical evidence linking weather factors and diarrheal disease burden in Nepal. This evidence suggests that additional climate change could increase diarrheal disease incidence across the nation. Mountainous regions are more sensitive to climate variability and consequently the burden of diarrheal diseases. These findings can be utilized to allocate necessary resources and envision a weather-based early warning system for the prevention and control of diarrheal diseases in Nepal.more » « less
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Wu, Joseph T. (Ed.)Colombia announced the first case of severe acute respiratory syndrome coronavirus 2 on March 6, 2020. Since then, the country has reported a total of 5,002,387 cases and 127,258 deaths as of October 31, 2021. The aggressive transmission dynamics of SARS-CoV-2 motivate an investigation of COVID-19 at the national and regional levels in Colombia. We utilize the case incidence and mortality data to estimate the transmission potential and generate short-term forecasts of the COVID-19 pandemic to inform the public health policies using previously validated mathematical models. The analysis is augmented by the examination of geographic heterogeneity of COVID-19 at the departmental level along with the investigation of mobility and social media trends. Overall, the national and regional reproduction numbers show sustained disease transmission during the early phase of the pandemic, exhibiting sub-exponential growth dynamics. Whereas the most recent estimates of reproduction number indicate disease containment, with R t <1.0 as of October 31, 2021. On the forecasting front, the sub-epidemic model performs best at capturing the 30-day ahead COVID-19 trajectory compared to the Richards and generalized logistic growth model. Nevertheless, the spatial variability in the incidence rate patterns across different departments can be grouped into four distinct clusters. As the case incidence surged in July 2020, an increase in mobility patterns was also observed. On the contrary, a spike in the number of tweets indicating the stay-at-home orders was observed in November 2020 when the case incidence had already plateaued, indicating the pandemic fatigue in the country.more » « less
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Adrish, Muhammad (Ed.)Mexico has experienced one of the highest COVID-19 mortality rates in the world. A delayed implementation of social distancing interventions in late March 2020 and a phased reopening of the country in June 2020 has facilitated sustained disease transmission in the region. In this study we systematically generate and compare 30-day ahead forecasts using previously validated growth models based on mortality trends from the Institute for Health Metrics and Evaluation for Mexico and Mexico City in near real-time. Moreover, we estimate reproduction numbers for SARS-CoV-2 based on the methods that rely on genomic data as well as case incidence data. Subsequently, functional data analysis techniques are utilized to analyze the shapes of COVID-19 growth rate curves at the state level to characterize the spatiotemporal transmission patterns of SARS-CoV-2. The early estimates of the reproduction number for Mexico were estimated between R t ~1.1–1.3 from the genomic and case incidence data. Moreover, the mean estimate of R t has fluctuated around ~1.0 from late July till end of September 2020. The spatial analysis characterizes the state-level dynamics of COVID-19 into four groups with distinct epidemic trajectories based on epidemic growth rates. Our results show that the sequential mortality forecasts from the GLM and Richards model predict a downward trend in the number of deaths for all thirteen forecast periods for Mexico and Mexico City. However, the sub-epidemic and IHME models perform better predicting a more realistic stable trajectory of COVID-19 mortality trends for the last three forecast periods (09/21-10/21, 09/28-10/27, 09/28-10/27) for Mexico and Mexico City. Our findings indicate that phenomenological models are useful tools for short-term epidemic forecasting albeit forecasts need to be interpreted with caution given the dynamic implementation and lifting of social distancing measures.more » « less
