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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.

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 Simple phenomenological growth models can be useful for estimating transmission parameters and forecasting epidemic trajectories. However, most existing phenomenological growth models only support single-peak outbreak dynamics whereas real epidemics often display more complex transmission trajectories. Methods We develop and apply a novel sub-epidemic modeling framework that supports a diversity of epidemic trajectories including stable incidence patterns with sustained or damped oscillations to better understand and forecast epidemic outbreaks. We describe how to forecast an epidemic based on the premise that the observed coarse-scale incidence can be decomposed into overlapping sub - epidemics at finer scales. We evaluate our modeling framework using three outbreak datasets: Severe Acute Respiratory Syndrome (SARS) in Singapore, plague in Madagascar, and the ongoing Ebola outbreak in the Democratic Republic of Congo (DRC) and four performance metrics. Results The sub-epidemic wave model outperforms simpler growth models in short-term forecasts based on performance metrics that account for the uncertainty of the predictions namely the mean interval score (MIS) and the coverage of the 95% prediction interval. For example, we demonstrate how the sub-epidemic wave model successfully captures the 2-peak pattern of the SARS outbreak in Singapore. Moreover, in short-term sequential forecasts, the sub-epidemic model was able to forecast the second surge in case incidence for this outbreak, which was not possible using the simple growth models. Furthermore, our findings support the view that the national incidence curve of the Ebola epidemic in DRC follows a stable incidence pattern with periodic behavior that can be decomposed into overlapping sub-epidemics. Conclusions Our findings highlight how overlapping sub-epidemics can capture complex epidemic dynamics, including oscillatory behavior in the trajectory of the epidemic wave. This observation has significant implications for interpreting apparent noise in incidence data where the oscillations could be dismissed as a result of overdispersion, rather than an intrinsic part of the epidemic dynamics. Unless the oscillations are appropriately modeled, they could also give a false positive, or negative, impression of the impact from public health interventions. These preliminary results using sub-epidemic models can help guide future efforts to better understand the heterogenous spatial and social factors shaping sub-epidemic patterns for other infectious diseases.

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.

The COVID-19 pandemic is one of the contagious diseases involving all the world in 2019–2020. Also, all people are concerned about the future of this catastrophe and how the continuous outbreak can be prevented. Some countries are not successful in controlling the outbreak; therefore, the incidence is observed in several peaks. In this paper, firstly single-peak SIR models are used for historical data. Regarding the SIR model, the termination time of the outbreak should have been in early June 2020. However, several peaks invalidate the results of single-peak models. Therefore, we should present a model to support pandemics with several extrema. In this paper, we presented the generalized logistic growth model (GLM) to estimate sub-epidemic waves of the COVID-19 outbreak in Iran. Therefore, the presented model simulated scenarios of two, three, and four waves in the observed incidence. In the second part of the paper, we assessed travel-related risk in inter-provincial travels in Iran. Moreover, the results of travel-related risk show that typical travel between Tehran and other sites exposed Isfahan, Gilan, Mazandaran, and West Azerbaijan in the higher risk of infection greater than 100 people per day. Therefore, controlling this movement can prevent great numbers of infection, remarkably.

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.

Australia’s response to the human immunodeficiency virus type 1 (HIV-1) pandemic led to effective control of HIV transmission and one of the world’s lowest HIV incidence rates—0.14%. Although there has been a recent decline in new HIV diagnoses in New South Wales (NSW), the most populous state in Australia, there has been a concomitant increase with non-B subtype infections, particularly for the HIV-1 circulating recombinant form CRF01_(A)E. This aforementioned CRF01_(A)E sampled in NSW, were combined with those sampled globally to identify NSW-specific viral clades. The population growth of these clades was assessed in two-year period intervals from 2009 to 2017. Overall, 109 NSW-specific clades were identified, most comprising pairs of sequences; however, five large clades comprising ≥10 sequences were also found. Forty-four clades grew over time with one or two sequences added to each in different two-year periods. Importantly, while 10 of these clades have seemingly discontinued, the remaining 34 were still active in 2016/2017. Seven such clades each comprised ≥10 sequences, and are representative of individual sub-epidemics in NSW. Thus, although the majority of new CRF01_(A)E infections were associated with small clades that rarely establish ongoing chains of local transmission, individual sub-epidemics are present and should be closely monitored.

Australia’s response to the human immunodeficiency virus type 1 (HIV-1) pandemic led to effective control of HIV transmission and one of the world’s lowest HIV incidence rates—0.14%. Although there has been a recent decline in new HIV diagnoses in New South Wales (NSW), the most populous state in Australia, there has been a concomitant increase with non-B subtype infections, particularly for the HIV-1 circulating recombinant form CRF01_AE. This aforementioned CRF01_AE sampled in NSW, were combined with those sampled globally to identify NSW-specific viral clades. The population growth of these clades was assessed in two-year period intervals from 2009 to 2017. Overall, 109 NSW-specific clades were identified, most comprising pairs of sequences; however, five large clades comprising ≥10 sequences were also found. Forty-four clades grew over time with one or two sequences added to each in different two-year periods. Importantly, while 10 of these clades have seemingly discontinued, the remaining 34 were still active in 2016/2017. Seven such clades each comprised ≥10 sequences, and are representative of individual sub-epidemics in NSW. Thus, although the majority of new CRF01_AE infections were associated with small clades that rarely establish ongoing chains of local transmission, individual sub-epidemics are present and should be closely monitored.

The canonical susceptible–infected–recovered (SIR) epidemic model is ubiquitous in assessing severity to guide interventions. It is typically applied to hierarchically aggregated data from distinct sub-regions. The introduced heterogeneity can lead to significant errors in estimated epidemic severity. We develop three analytical methods to extract SIR parameters from data, focusing on the reproduction number R0 that quantifies epidemic wave severity/strength. The estimation methods are applied to synthetically aggregated incidence data formulated by summing two independent SIR solutions of distinct R0 and separated by an onset delay, i.e. temporal offset. When applying the SIR model, we find that R0 estimates from the aggregated data can underestimate or overestimate the constituent epidemic waves’ R0 even when the prediction appears to agree well with the incidence data, resulting in an erroneous unimodal epidemic dynamics. We find that for two epidemic waves, the stronger the trailing wave, the longer the temporal offset that maintains apparent erroneous unimodal aggregated data. In the special case of two equivalent epidemic strengths, however, the weaker the waves, the longer the offset that maintains apparent unimodal aggregated data. We provide sensitivity analyses with respect to noise perturbation of the data and illustrate our approach using historical influenza data.

This volume is a single up-to-date source on the entire global epidemiology of diseases, injuries and risk factors with a comprehensive statement of methods and a complete presentation of results. It includes refined methods to assess data, ensure epidemiological consistency, and summarize the disease burden. Global Burden of Disease and Risk Factors examines the comparative importance of diseases, injuries, and risk factors; it incorporates a range of new data sources to develop consistent estimates of incidence, prevalence, severity and duration, and mortality for 136 major diseases and injuries. Drawing from more than 8,500 data sources that include epidemiological studies, disease registers, and notifications systems, Global Burden of Disease and Risk Factors incorporates information from more than 10,000 datasets relating to population health and mortality, representing one of the largest syntheses of global information on population health to date.