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Abstract BackgroundDynamical 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. ResultsThis 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. ConclusionsWe 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. 

Metagenomics has revolutionized our understanding of microbial communities, offering unprecedented insights into their genetic and functional diversity across Earth’s diverse ecosystems. Beyond their roles as environmental constituents, microbiomes act as symbionts, profoundly influencing the health and function of their host organisms. Given the inherent complexity of these communities and the diverse environments where they reside, the components of a metagenomics study must be carefully tailored to yield accurate results that are representative of the populations of interest. This Primer examines the methodological advancements and current practices that have shaped the field, from initial stages of sample collection and DNA extraction to the advanced bioinformatics tools employed for data analysis, with a particular focus on the profound impact of next-generation sequencing on the scale and accuracy of metagenomics studies. We critically assess the challenges and limitations inherent in metagenomics experimentation, available technologies and computational analysis methods. Beyond technical methodologies, we explore the application of metagenomics across various domains, including human health, agriculture and environmental monitoring. Looking ahead, we advocate for the development of more robust computational frameworks and enhanced interdisciplinary collaborations. This Primer serves as a comprehensive guide for advancing the precision and applicability of metagenomic studies, positioning them to address the complexities of microbial ecology and their broader implications for human health and environmental sustainability. 

The 2022–2023 mpox outbreak exhibited an uneven global distribution. While countries such as the UK, Brazil, and the USA were most heavily affected in 2022, many Asian countries, specifically China, Japan, South Korea, and Thailand, experienced the outbreak later, in 2023, with significantly fewer reported cases relative to their populations. This variation in timing and scale distinguishes the outbreaks in these Asian countries from those in the first wave. This study evaluates the predictability of mpox outbreaks with smaller case counts in Asian countries using popular epidemic forecasting methods, including the ARIMA, Prophet, GLM, GAM, n-Sub-epidemic, and Sub-epidemic Wave frameworks. Despite the fact that the ARIMA and GAM models performed well for certain countries and prediction windows, their results were generally inconsistent and highly dependent on the country, i.e., the dataset, as well as the prediction interval length. In contrast, n-Sub-epidemic Ensembles demonstrated more reliable and robust performance across different datasets and predictions, indicating the effectiveness of this model on small datasets and its utility in the early stages of future pandemics. 

The integration of viral genomic data into public health surveillance has revolutionized our ability to track and forecast infectious disease dynamics. This review addresses two critical aspects of infectious disease forecasting and monitoring: the methodological workflow for epidemic forecasting and the transformative role of molecular surveillance. We first present a detailed approach for validating epidemic models, emphasizing an iterative workflow that utilizes ordinary differential equation (ODE)-based models to investigate and forecast disease dynamics. We recommend a more structured approach to model validation, systematically addressing key stages such as model calibration, assessment of structural and practical parameter identifiability, and effective uncertainty propagation in forecasts. Furthermore, we underscore the importance of incorporating multiple data streams by applying both simulated and real epidemiological data from the COVID-19 pandemic to produce more reliable forecasts with quantified uncertainty. Additionally, we emphasize the pivotal role of viral genomic data in tracking transmission dynamics and pathogen evolution. By leveraging advanced computational tools such as Bayesian phylogenetics and phylodynamics, researchers can more accurately estimate transmission clusters and reconstruct outbreak histories, thereby improving data-driven modeling and forecasting and informing targeted public health interventions. Finally, we discuss the transformative potential of integrating molecular epidemiology with mathematical modeling to complement and enhance epidemic forecasting and optimize public health strategies. 

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 andn-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, then-sub-epidemic modelling framework outcompeted other models across most locations and forecasting horizons, with the unweighted ensemble model performing best most frequently. Then-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.