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Since December 2019, when the first case of coronavirus disease (COVID-19) was identified in the city of Wuhan in the Hubei Province of China, the epidemic has generated tens of thousands of cases throughout China. As of February 28, 2020, the cumulative number of reported deaths in China was 2,858. We estimated the time-delay adjusted risk for death from COVID-19 in Wuhan, as well as for China excluding Wuhan, to assess the severity of the epidemic in the country. Our estimates of the risk for death in Wuhan reached values as high as 12% in the epicenter of the epidemic and ≈1% in other, more mildly affected areas. The elevated death risk estimates are probably associated with a breakdown of the healthcare system, indicating that enhanced public health interventions, including social distancing and movement restrictions, should be implemented to bring the COVID-19 epidemic under control.

The complex and unprecedented Ebola epidemic ongoing in West Africa has highlighted the need to review the epidemiological characteristics of Ebola Virus Disease (EVD) as well as our current understanding of the transmission dynamics and the effect of control interventions against Ebola transmission. Here we review key epidemiological data from past Ebola outbreaks and carry out a comparative review of mathematical models of the spread and control of Ebola in the context of past outbreaks and the ongoing epidemic in West Africa. We show that mathematical modeling offers useful insights into the risk of a major epidemic of EVD and the assessment of the impact of basic public health measures on disease spread. We also discuss the critical need to collect detailed epidemiological data in real-time during the course of an ongoing epidemic, carry out further studies to estimate the effectiveness of interventions during past outbreaks and the ongoing epidemic, and develop large-scale modeling studies to study the spread and control of viral hemorrhagic fevers in the context of the highly heterogeneous economic reality of African countries.

COVID-19 vaccines have been authorized in multiple countries, and more are under rapid development. Careful design of a vaccine prioritization strategy across sociodemographic groups is a crucial public policy challenge given that 1) vaccine supply will be constrained for the first several months of the vaccination campaign, 2) there are stark differences in transmission and severity of impacts from severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) across groups, and 3) SARS-CoV-2 differs markedly from previous pandemic viruses. We assess the optimal allocation of a limited vaccine supply in the United States across groups differentiated by age and essential worker status, which constrains opportunities for social distancing. We model transmission dynamics using a compartmental model parameterized to capture current understanding of the epidemiological characteristics of COVID-19, including key sources of group heterogeneity (susceptibility, severity, and contact rates). We investigate three alternative policy objectives (minimizing infections, years of life lost, or deaths) and model a dynamic strategy that evolves with the population epidemiological status. We find that this temporal flexibility contributes substantially to public health goals. Older essential workers are typically targeted first. However, depending on the objective, younger essential workers are prioritized to control spread or seniors to directly control mortality. When the objective is minimizing deaths, relative to an untargeted approach, prioritization averts deaths on a range between 20,000 (when nonpharmaceutical interventions are strong) and 300,000 (when these interventions are weak). We illustrate how optimal prioritization is sensitive to several factors, most notably, vaccine effectiveness and supply, rate of transmission, and the magnitude of initial infections.

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.

Deterministic and stochastic methods relying on early case incidence data for forecasting epidemic outbreaks have received increasing attention during the last few years. In mathematical terms, epidemic forecasting is an ill-posed problem due to instability of parameter identification and limited available data. While previous studies have largely estimated the time-dependent transmission rate by assuming specific functional forms (e.g., exponential decay) that depend on a few parameters, here we introduce a novel approach for the reconstruction of nonparametric time-dependent transmission rates by projecting onto a finite subspace spanned by Legendre polynomials. This approach enables us to effectively forecast future incidence cases, the clear advantage over recovering the transmission rate at finitely many grid points within the interval where the data are currently available. In our approach, we compare three regularization algorithms: variational (Tikhonov’s) regularization, truncated singular value decomposition (TSVD), and modified TSVD in order to determine the stabilizing strategy that is most effective in terms of reliability of forecasting from limited data. We illustrate our methodology using simulated data as well as case incidence data for various epidemics including the 1918 influenza pandemic in San Francisco and the 2014–2015 Ebola epidemic in West Africa.

AbstractObjectiveTo evaluate the association between physical distancing interventions and incidence of coronavirus disease 2019 (covid-19) globally.DesignNatural experiment using interrupted time series analysis, with results synthesised using meta-analysis.Setting149 countries or regions, with data on daily reported cases of covid-19 from the European Centre for Disease Prevention and Control and data on the physical distancing policies from the Oxford covid-19 Government Response Tracker.ParticipantsIndividual countries or regions that implemented one of the five physical distancing interventions (closures of schools, workplaces, and public transport, restrictions on mass gatherings and public events, and restrictions on movement (lockdowns)) between 1 January and 30 May 2020.Main outcome measureIncidence rate ratios (IRRs) of covid-19 before and after implementation of physical distancing interventions, estimated using data to 30 May 2020 or 30 days post-intervention, whichever occurred first. IRRs were synthesised across countries using random effects meta-analysis.ResultsOn average, implementation of any physical distancing intervention was associated with an overall reduction in covid-19 incidence of 13% (IRR 0.87, 95% confidence interval 0.85 to 0.89; n=149 countries). Closure of public transport was not associated with any additional reduction in covid-19 incidence when the other four physical distancing interventions were in place (pooled IRR with and without public transport closure was 0.85, 0.82 to 0.88; n=72, and 0.87, 0.84 to 0.91; n=32, respectively). Data from 11 countries also suggested similar overall effectiveness (pooled IRR 0.85, 0.81 to 0.89) when school closures, workplace closures, and restrictions on mass gatherings were in place. In terms of sequence of interventions, earlier implementation of lockdown was associated with a larger reduction in covid-19 incidence (pooled IRR 0.86, 0.84 to 0.89; n=105) compared with a delayed implementation of lockdown after other physical distancing interventions were in place (pooled IRR 0.90, 0.87 to 0.94; n=41).ConclusionsPhysical distancing interventions were associated with reductions in the incidence of covid-19 globally. No evidence was found of an additional effect of public transport closure when the other four physical distancing measures were in place. Earlier implementation of lockdown was associated with a larger reduction in the incidence of covid-19. These findings might support policy decisions as countries prepare to impose or lift physical distancing measures in current or future epidemic waves.

We devote a special issue of the Journal of Infectious Diseases to review the recent advances of big data in strengthening disease surveillance, monitoring medical adverse events, informing transmission models, and tracking patient sentiments and mobility. We consider a broad definition of big data for public health, one encompassing patient information gathered from high-volume electronic health records and participatory surveillance systems, as well as mining of digital traces such as social media, Internet searches, and cell-phone logs. We introduce nine independent contributions to this special issue and highlight several cross-cutting areas that require further research, including representativeness, biases, volatility, and validation, and the need for robust statistical and hypotheses-driven analyses. Overall, we are optimistic that the big-data revolution will vastly improve the granularity and time-liness of available epidemiological information, with hybrid systems augmenting rather than supplanting traditional surveillance systems, and better prospects for accurate infectious diseases models and forecasts.

Background Since the first cluster of cases was identified in Wuhan City, China, in December 2019, coronavirus disease 2019 (COVID-19) rapidly spreads globally. Scientists have made strides in estimating key transmission and epidemiological parameters. In particular, accumulating evidence points to a substantial fraction of asymptomatic or subclinical infections, which influences our understanding of the transmission potential and severity of this emerging disease. In this study, we derive estimates of the transmissibility and virulence of COVID-19 in Wuhan City, China, by reconstructing the underlying transmission dynamics using multiple data sources. Methods We employ statistical methods and publicly available epidemiological datasets to jointly derive estimates of transmissibility and severity associated with the novel coronavirus. For this purpose, the daily series of laboratory-confirmed COVID-19 cases and deaths in Wuhan City together with epidemiological data of Japanese repatriated from Wuhan City on board government-chartered flights were integrated into our analysis. Results Our posterior estimates of basic reproduction number ( R ) in Wuhan City, China, in 2019–2020 reached values at 3.49 (95% CrI 3.39–3.62) with a mean serial interval of 6.0 days, and the enhanced public health intervention after January 23 in 2020 was associated with a significantly reduced R at 0.84 (95% CrI 0.81–0.88), with the total number of infections (i.e., cumulative infections) estimated at 1,906,634 (95% CrI 1,373,500–2,651,124) in Wuhan City, elevating the overall proportion of infected individuals to 19.1% (95% CrI 13.5–26.6%). We also estimated the most recent crude infection fatality ratio (IFR) and time–delay adjusted IFR at 0.04% (95% CrI 0.03–0.06%) and 0.12% (95% CrI 0.08–0.17%), respectively, estimates that are substantially smaller than the crude CFR estimated at 4.06%. Conclusions We have estimated key epidemiological parameters of the transmissibility and virulence of COVID-19 in Wuhan, China, during January–February 2020 using an ecological modeling approach that is suitable to infer epidemiological parameters with quantified uncertainty from partial observations collected by surveillance systems. Our estimate of time–delay adjusted IFR falls in the range of the median IFR estimates based on multiple serological studies conducted in several areas of the world.

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.