Practical considerations for measuring the effective reproductive number, Rt

Trajectories of COVID-19: A longitudinal analysis of many nations and subnational regions

The COVID-19 pandemic is the first to be rapidly and sequentially measured by nation-wide PCR community testing for the presence of the viral RNA at a global scale. We take advantage of the novel "natural experiment" where diverse nations and major subnational regions implemented various policies including social distancing and vaccination at different times with different levels of stringency and adherence. Initially, case numbers expand exponentially with doubling times of ~1-2 weeks. In the nations where interventions were not implemented or perhaps lees effectual, case numbers increased exponentially but then stabilized around 102-to-103 new infections (per km2 built-up area per day). Dynamics under effective interventions were perturbed and infections decayed to low levels. They rebounded concomitantly with the lifting of social distancing policies or pharmaceutical efficacy decline, converging on a stable equilibrium setpoint. Here we deploy a mathematical model which captures this V-shape behavior, incorporating a direct measure of intervention efficacy. Importantly, it allows the derivation of a maximal estimate for the basic reproductive number Ro (mean 1.6-1.8). We were able to test this approach by comparing the approximated "herd immunity" to the vaccination coverage observed that corresponded to rapid declines in community infections during 2021. The estimates reported here agree with the observed phenomena. Moreover, the decay (0.4-0.5) and rebound rates (0.2-0.3) were similar throughout the pandemic and among all the nations and regions studied. Finally, a longitudinal analysis comparing multiple national and regional results provides insights on the underlying epidemiology of SARS-CoV-2 and intervention efficacy, as well as evidence for the existence of an endemic steady state of COVID-19.

Multivariate epidemic count time series model

An infectious disease spreads not only over a single population or community but also across multiple and heterogeneous communities. Moreover, its transmissibility varies over time because of various factors such as seasonality and epidemic control, which results in strongly nonstationary behavior. In conventional methods for assessing transmissibility trends or changes, univariate time-varying reproduction numbers are calculated without taking into account transmission across multiple communities. In this paper, we propose a multivariate-count time series model for epidemics. We also propose a statistical method for estimating the transmission of infections across multiple communities and the time-varying reproduction numbers of each community simultaneously from a multivariate time series of case counts. We apply our method to incidence data for the novel coronavirus disease 2019 (COVID-19) pandemic to reveal the spatiotemporal heterogeneity of the epidemic process.

Key epidemiological indicators and spatial autocorrelation patterns across five waves of COVID-19 in Catalonia

This research studies the evolution of COVID-19 crude incident rates, effective reproduction number R(t) and their relationship with incidence spatial autocorrelation patterns in the 19 months following the disease outbreak in Catalonia (Spain). A cross-sectional ecological panel design based on n = 371 health-care geographical units is used. Five general outbreaks are described, systematically preceded by generalized values of R(t) > 1 in the two previous weeks. No clear regularities concerning possible initial focus appear when comparing waves. As for autocorrelation, we identify a wave's baseline pattern in which global Moran's I increases rapidly in the first weeks of the outbreak to descend later. However, some waves significantly depart from the baseline. In the simulations, both baseline pattern and departures can be reproduced when measures aimed at reducing mobility and virus transmissibility are introduced. Spatial autocorrelation is inherently contingent on the outbreak phase and is also substantially modified by external interventions affecting human behavior.

No evidence of sustained nonzoonotic Plasmodium knowlesi transmission in Malaysia from modelling malaria case data

Reported incidence of the zoonotic malaria Plasmodium knowlesi has markedly increased across Southeast Asia and threatens malaria elimination. Nonzoonotic transmission of P. knowlesi has been experimentally demonstrated, but it remains unknown whether nonzoonotic transmission is contributing to increases in P. knowlesi cases. Here, we adapt model-based inference methods to estimate RC, individual case reproductive numbers, for P. knowlesi, P. falciparum and P. vivax human cases in Malaysia from 2012-2020 (n = 32,635). Best fitting models for P. knowlesi showed subcritical transmission (RC < 1) consistent with a large reservoir of unobserved infection sources, indicating P. knowlesi remains a primarily zoonotic infection. In contrast, sustained transmission (RC > 1) was estimated historically for P. falciparum and P. vivax, with declines in RC estimates observed over time consistent with local elimination. Together, this suggests sustained nonzoonotic P. knowlesi transmission is highly unlikely and that new approaches are urgently needed to control spillover risks.

Identification of growing tuberculosis incidence clusters in a region with a decrease in tuberculosis prevalence in Moscow (2000-2019)

Background

The control of tuberculosis (TB) may benefit from a prospective identification of areas where the incidence may increase in addition to the traditionally identified foci of high incidence. We aimed to identify residential areas with growing tuberculosis incidence rates and assess their significance and stability.

Methods

We analysed the changes in TB incidence rates using case data georeferenced with spatial granularity to apartment buildings in the territory of Moscow from 2000 to 2019. We identified sparsely distributed areas with significant increases in the incidence rate inside residential areas. We tested the stability of found growth areas to case underreporting via stochastic modelling.

Results

For 21 350 cases with smear- or culture-positive pulmonary TB among residents from 2000 to 2019, we identified 52 small-scale clusters of growing incidence rate responsible for 1% of all registered cases. We tested clusters of disease growth for underreporting and found them to be relatively unstable to resampling with case drop-out, but their spatial displacement was small. Territories with a stable increase in TB incidence rate were identified and compared to the rest of the city, which is characterised by a significant decrease in incidence.

Conclusions

Identified areas with a tendency for an increase in the TB incidence rate may be important targets for disease control services.

Design of effective outpatient sentinel surveillance for COVID-19 decision-making: a modeling study

BACKGROUND

Decision-makers impose COVID-19 mitigations based on public health indicators such as reported cases, which are sensitive to fluctuations in supply and demand for diagnostic testing, and hospital admissions, which lag infections by up to two weeks. Imposing mitigations too early has unnecessary economic costs while imposing too late leads to uncontrolled epidemics with unnecessary cases and deaths. Sentinel surveillance of recently-symptomatic individuals in outpatient testing sites may overcome biases and lags in conventional indicators, but the minimal outpatient sentinel surveillance system needed for reliable trend estimation remains unknown.

METHODS

We used a stochastic, compartmental transmission model to evaluate the performance of various surveillance indicators at reliably triggering an alarm in response to, but not before, a step increase in transmission of SARS-CoV-2. The surveillance indicators included hospital admissions, hospital occupancy, and sentinel cases with varying levels of sampling effort capturing 5, 10, 20, 50, or 100% of incident mild cases. We tested 3 levels of transmission increase, 3 population sizes, and conditions of either simultaneous transmission increase or lagged increase in the older population. We compared the indicators' performance at triggering alarm soon after, but not prior, to the transmission increase.

RESULTS

Compared to surveillance based on hospital admissions, outpatient sentinel surveillance that captured at least 20% of incident mild cases could trigger an alarm 2 to 5 days earlier for a mild increase in transmission and 6 days earlier for a moderate or strong increase. Sentinel surveillance triggered fewer false alarms and averted more deaths per day spent in mitigation. When transmission increase in older populations lagged the increase in younger populations by 14 days, sentinel surveillance extended its lead time over hospital admissions by an additional 2 days.

CONCLUSIONS

Sentinel surveillance of mild symptomatic cases can provide more timely and reliable information on changes in transmission to inform decision-makers in an epidemic like COVID-19.

Effectiveness assessment of non-pharmaceutical interventions: lessons learned from the COVID-19 pandemic

Effectiveness of non-pharmaceutical interventions (NPIs), such as school closures and stay-at-home orders, during the COVID-19 pandemic has been assessed in many studies. Such assessments can inform public health policies and contribute to evidence-based choices of NPIs during subsequent waves or future epidemics. However, methodological issues and no standardised assessment practices have restricted the practical value of the existing evidence. Here, we present and discuss lessons learned from the COVID-19 pandemic and make recommendations for standardising and improving assessment, data collection, and modelling. These recommendations could contribute to reliable and policy-relevant assessments of the effectiveness of NPIs during future epidemics.

A new method for the joint estimation of instantaneous reproductive number and serial interval during epidemics

Although some methods for estimating the instantaneous reproductive number during epidemics have been developed, the existing frameworks usually require information on the distribution of the serial interval and/or additional contact tracing data. However, in the case of outbreaks of emerging infectious diseases with an unknown natural history or undetermined characteristics, the serial interval and/or contact tracing data are often not available, resulting in inaccurate estimates for this quantity. In the present study, a new framework was specifically designed for joint estimates of the instantaneous reproductive number and serial interval. Concretely, a likelihood function for the two quantities was first introduced. Then, the instantaneous reproductive number and the serial interval were modeled parametrically as a function of time using the interpolation method and a known traditional distribution, respectively. Using the Bayesian information criterion and the Markov Chain Monte Carlo method, we ultimately obtained their estimates and distribution. The simulation study revealed that our estimates of the two quantities were consistent with the ground truth. Seven data sets of historical epidemics were considered and further verified the robust performance of our method. Therefore, to some extent, even if we know only the daily incidence, our method can accurately estimate the instantaneous reproductive number and serial interval to provide crucial information for policymakers to design appropriate prevention and control interventions during epidemics.

Impact of non-pharmaceutical interventions, weather, vaccination, and variants on COVID-19 transmission across departments in France

BACKGROUND

Multiple factors shape the temporal dynamics of the COVID-19 pandemic. Quantifying their relative contributions is key to guide future control strategies. Our objective was to disentangle the individual effects of non-pharmaceutical interventions (NPIs), weather, vaccination, and variants of concern (VOC) on local SARS-CoV-2 transmission.

METHODS

We developed a log-linear model for the weekly reproduction number (R) of hospital admissions in 92 French metropolitan departments. We leveraged (i) the homogeneity in data collection and NPI definitions across departments, (ii) the spatial heterogeneity in the timing of NPIs, and (iii) an extensive observation period (14 months) covering different weather conditions, VOC proportions, and vaccine coverage levels.

FINDINGS

Three lockdowns reduced R by 72.7% (95% CI 71.3-74.1), 70.4% (69.2-71.6) and 60.7% (56.4-64.5), respectively. Curfews implemented at 6/7 pm and 8/9 pm reduced R by 34.3% (27.9-40.2) and 18.9% (12.04-25.3), respectively. School closures reduced R by only 4.9% (2.0-7.8). We estimated that vaccination of the entire population would have reduced R by 71.7% (56.4-81.6), whereas the emergence of VOC (mainly Alpha during the study period) increased transmission by 44.6% (36.1-53.6) compared with the historical variant. Winter weather conditions (lower temperature and absolute humidity) increased R by 42.2% (37.3-47.3) compared to summer weather conditions. Additionally, we explored counterfactual scenarios (absence of VOC or vaccination) to assess their impact on hospital admissions.

INTERPRETATION

Our study demonstrates the strong effectiveness of NPIs and vaccination and quantifies the role of weather while adjusting for other confounders. It highlights the importance of retrospective evaluation of interventions to inform future decision-making.

Spatiotemporal reproduction number with Bayesian model selection for evaluation of emerging infectious disease transmissibility: an application to COVID-19 national surveillance data

BACKGROUND

To control emerging diseases, governments often have to make decisions based on limited evidence. The effective or temporal reproductive number is used to estimate the expected number of new cases caused by an infectious person in a partially susceptible population. While the temporal dynamic is captured in the temporal reproduction number, the dominant approach is currently based on modeling that implicitly treats people within a population as geographically well mixed.

METHODS

In this study we aimed to develop a generic and robust methodology for estimating spatiotemporal dynamic measures that can be instantaneously computed for each location and time within a Bayesian model selection and averaging framework. A simulation study was conducted to demonstrate robustness of the method. A case study was provided of a real-world application to COVID-19 national surveillance data in Thailand.

RESULTS

Overall, the proposed method allowed for estimation of different scenarios of reproduction numbers in the simulation study. The model selection chose the true serial interval when included in our study whereas model averaging yielded the weighted outcome which could be less accurate than model selection. In the case study of COVID-19 in Thailand, the best model based on model selection and averaging criteria had a similar trend to real data and was consistent with previously published findings in the country.

CONCLUSIONS

The method yielded robust estimation in several simulated scenarios of force of transmission with computing flexibility and practical benefits. Thus, this development can be suitable and practically useful for surveillance applications especially for newly emerging diseases. As new outbreak waves continue to develop and the risk changes on both local and global scales, our work can facilitate policymaking for timely disease control.

Evolving Drivers of Brazilian SARS-CoV-2 Transmission: A Spatiotemporally Disaggregated Time Series Analysis of Meteorology, Policy, and Human Mobility

Brazil has been severely affected by the COVID-19 pandemic. Temperature and humidity have been purported as drivers of SARS-CoV-2 transmission, but no consensus has been reached in the literature regarding the relative roles of meteorology, governmental policy, and mobility on transmission in Brazil. We compiled data on meteorology, governmental policy, and mobility in Brazil's 26 states and one federal district from June 2020 to August 2021. Associations between these variables and the time-varying reproductive number (R _t ) of SARS-CoV-2 were examined using generalized additive models fit to data from the entire 15-month period and several shorter, 3-month periods. Accumulated local effects and variable importance metrics were calculated to analyze the relationship between input variables and R _t . We found that transmission is strongly influenced by unmeasured sources of between-state heterogeneity and the near-recent trajectory of the pandemic. Increased temperature generally was associated with decreased transmission and increased specific humidity with increased transmission. However, the impacts of meteorology, policy, and mobility on R _t varied in direction, magnitude, and significance across our study period. This time variance could explain inconsistencies in the published literature to date. While meteorology weakly modulates SARS-CoV-2 transmission, daily or seasonal weather variations alone will not stave off future surges in COVID-19 cases in Brazil. Investigating how the roles of environmental factors and disease control interventions may vary with time should be a deliberate consideration of future research on the drivers of SARS-CoV-2 transmission.

Real-time estimation and forecasting of COVID-19 cases and hospitalizations in Wisconsin HERC regions for public health decision making processes

BACKGROUND

The spread of the COVID-19 (SARS-CoV-2) and the surging number of cases across the United States have resulted in full hospitals and exhausted health care workers. Limited availability and questionable reliability of the data make outbreak prediction and resource planning difficult. Any estimates or forecasts are subject to high uncertainty and low accuracy to measure such components. The aim of this study is to apply, automate, and assess a Bayesian time series model for the real-time estimation and forecasting of COVID-19 cases and number of hospitalizations in Wisconsin healthcare emergency readiness coalition (HERC) regions.

METHODS

This study makes use of the publicly available Wisconsin COVID-19 historical data by county. Cases and effective time-varying reproduction number [Formula: see text] by the HERC region over time are estimated using Bayesian latent variable models. Hospitalizations are estimated by the HERC region over time using a Bayesian regression model. Cases, effective Rt, and hospitalizations are forecasted over a 1-day, 3-day, and 7-day time horizon using the last 28 days of data, and the 20%, 50%, and 90% Bayesian credible intervals of the forecasts are calculated. The frequentist coverage probability is compared to the Bayesian credible level to evaluate performance.

RESULTS

For cases and effective [Formula: see text], all three time horizons outperform the three credible levels of the forecast. For hospitalizations, all three time horizons outperform the 20% and 50% credible intervals of the forecast. On the contrary, the 1-day and 3-day periods underperform the 90% credible intervals. Questions about uncertainty quantification should be re-calculated using the frequentist coverage probability of the Bayesian credible interval based on observed data for all three metrics.

CONCLUSIONS

We present an approach to automate the real-time estimation and forecasting of cases and hospitalizations and corresponding uncertainty using publicly available data. The models were able to infer short-term trends consistent with reported values at the HERC region level. Additionally, the models were able to accurately forecast and estimate the uncertainty of the measurements. This study can help identify the most affected regions and major outbreaks in the near future. The workflow can be adapted to other geographic regions, states, and even countries where decision-making processes are supported in real-time by the proposed modeling system.

SARS-CoV-2 spread and area economic disadvantage in the italian three-tier restrictions: a multilevel approach

BACKGROUND

To face the second wave of COVID-19, Italy implemented a tiered restriction system with different limitation levels (yellow = medium; orange = medium-high, red = high) at the beginning of November 2020. The restrictions systematically reduced the transmission of SARS-CoV-2 with increasing strength for increasing tier. However, it is unknown whether the effect of limitations was equal between provinces with different socioeconomic levels. Therefore, we investigated the association between the province's socioeconomic level and SARS-CoV-2 infection daily reproduction number in each restriction level.

METHODS

We measured the province's socioeconomic level as the percentage of individuals whose 2019 total yearly income was lower than 10,000€, using the measure as a proxy of economic disadvantage. We estimated the daily reproduction number (Rt) at the province level using the SARS-CoV-2 daily incidence data from November 2020 to May 2021. We then used multilevel linear regression models with random intercepts stratified by restriction level to estimate the association between economic disadvantage and Rt. We also adjusted the analyses for potential confounders of the association between the province's economic disadvantage and the Rt: the percentage of people with 0-5 years, the quartiles of population density, and the geographical repartition.

RESULTS

Overall, we found increasing Rt in yellow (+ 0.004 p < 0.01, from Rt = 0.99 to 1.08 in three weeks) and containing effects for the orange (-0.005 p < 0.01, from Rt = 1.03 to 0.93) and the red tier (-0.014 p < 0.01, from Rt = 1.05 to 0.76). More economically disadvantaged provinces had higher Rt levels in every tier, although non-significantly in the yellow level (yellow = 0.001 p = 0.19; orange = 0.002 p = 0.02; red = 0.004 p < 0.01). The results showed that the association between economic disadvantage and Rt differed by level of restriction. The number of days into the restriction and the economic disadvantage had statistically significant interactions in every adjusted model. Compared to better off, more economically disadvantaged provinces had slower increasing trends in yellow and steeper Rt reductions in orange, but they showed slower Rt reductions in the highest tier.

CONCLUSION

Lower tiers were more effective in more economically disadvantaged provinces, while the highest restriction level had milder effects. These results underline the importance of accounting for socioeconomic level when implementing public health measures.

A dynamic causal modeling of the second outbreak of COVID-19 in Italy

While the vaccination campaign against COVID-19 is having its positive impact, we retrospectively analyze the causal impact of some decisions made by the Italian government on the second outbreak of the SARS-CoV-2 pandemic in Italy, when no vaccine was available. First, we analyze the causal impact of reopenings after the first lockdown in 2020. In addition, we also analyze the impact of reopening schools in September 2020. Our results provide an unprecedented opportunity to evaluate the causal relationship between the relaxation of restrictions and the transmission in the community of a highly contagious respiratory virus that causes severe illness in the absence of prophylactic vaccination programs. We present a purely data-analytic approach based on a Bayesian methodology and discuss possible interpretations of the results obtained and implications for policy makers.

A Bayesian nonparametric method for detecting rapid changes in disease transmission

Whether an outbreak of infectious disease is likely to grow or dissipate is determined through the time-varying reproduction number, R_t. Real-time or retrospective identification of changes in R_t following the imposition or relaxation of interventions can thus contribute important evidence about disease transmission dynamics which can inform policymaking. Here, we present a method for estimating shifts in R_t within a renewal model framework. Our method, which we call EpiCluster, is a Bayesian nonparametric model based on the Pitman-Yor process. We assume that R_t is piecewise-constant, and the incidence data and priors determine when or whether R_t should change and how many times it should do so throughout the series. We also introduce a prior which induces sparsity over the number of changepoints. Being Bayesian, our approach yields a measure of uncertainty in R_t and its changepoints. EpiCluster is fast, straightforward to use, and we demonstrate that it provides automated detection of rapid changes in transmission, either in real-time or retrospectively, for synthetic data series where the R_t profile is known. We illustrate the practical utility of our method by fitting it to case data of outbreaks of COVID-19 in Australia and Hong Kong, where it finds changepoints coinciding with the imposition of non-pharmaceutical interventions. Bayesian nonparametric methods, such as ours, allow the volume and complexity of the data to dictate the number of parameters required to approximate the process and should find wide application in epidemiology. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Associations between greenness and predicted COVID-19-like illness incidence in the United States and the United Kingdom

Green spaces may be protective against COVID-19 incidence. They may provide outdoor, ventilated, settings for physical and social activities and therefore decrease transmission risk. We examined the association between neighborhood greenness and COVID-19-like illness incidence using individual-level data.

Methods

The study population includes participants enrolled in the COVID Symptom Study smartphone application in the United Kingdom and the United States (March-November 2020). All participants were encouraged to report their current health condition and suspected risk factors for COVID-19. We used a validated symptom-based classifier that predicts COVID-19-like illness. We estimated the Normalized Difference Vegetation Index (NDVI), for each participant's reported neighborhood of residence for each month, using images from Landsat 8 (30 m2). We used time-varying Cox proportional hazards models stratified by age, country, and calendar month at study entry and adjusted for the individual- and neighborhood-level risk factors.

Results

We observed 143,340 cases of predicted COVID-19-like illness among 2,794,029 participants. Neighborhood NDVI was associated with a decreased risk of predicted COVID-19-like illness incidence in the fully adjusted model (hazard ratio = 0.965, 95% confidence interval = 0.960, 0.970, per 0.1 NDVI increase). Stratified analyses showed protective associations among U.K. participants but not among U.S. participants. Associations were slightly stronger for White individuals, for individuals living in rural neighborhoods, and for individuals living in high-income neighborhoods compared to individuals living in low-income neighborhoods.

Conclusions

Higher levels of greenness may reduce the risk of predicted COVID-19-like illness incidence, but these associations were not observed in all populations.

Analysis of COVID-19 in Japan with extended SEIR model and ensemble Kalman filter

We introduce an extended SEIR infectious disease model with data assimilation for the study of the spread of COVID-19. In this framework, undetected asymptomatic and pre-symptomatic cases are taken into account, and the impact of their uncertain proportion is fully investigated. The standard SEIR model does not consider these populations, while their role in the propagation of the disease is acknowledged. An ensemble Kalman filter is implemented to assimilate reliable observations of three compartments in the model. The system tracks the evolution of the effective reproduction number and estimates the unobservable subpopulations. The analysis is carried out for three main prefectures of Japan and for the entire country of Japan. For these four communities, our estimated effective reproduction numbers are more stable than the corresponding ones estimated by a different method (Toyokeizai). We also perform sensitivity tests for different values of some uncertain medical parameters, like the relative infectivity of symptomatic/asymptomatic cases. The regional analysis results suggest the decreasing efficiency of the states of emergency.

Modelling the impact of the Omicron BA.5 subvariant in New Zealand

New Zealand experienced a wave of the Omicron variant of SARS-CoV-2 in early 2022, which occurred against a backdrop of high two-dose vaccination rates, ongoing roll-out of boosters and paediatric doses, and negligible levels of prior infection. New Omicron subvariants have subsequently emerged with a significant growth advantage over the previously dominant BA.2. We investigated a mathematical model that included waning of vaccine-derived and infection-derived immunity, as well as the impact of the BA.5 subvariant which began spreading in New Zealand in May 2022. The model was used to provide scenarios to the New Zealand Government with differing levels of BA.5 growth advantage, helping to inform policy response and healthcare system preparedness during the winter period. In all scenarios investigated, the projected peak in new infections during the BA.5 wave was smaller than in the first Omicron wave in March 2022. However, results indicated that the peak hospital occupancy was likely to be higher than in March 2022, primarily due to a shift in the age distribution of infections to older groups. We compare model results with subsequent epidemiological data and show that the model provided a good projection of cases, hospitalizations and deaths during the BA.5 wave.

A modelling approach to estimate the transmissibility of SARS-CoV-2 during periods of high, low, and zero case incidence

Against a backdrop of widespread global transmission, a number of countries have successfully brought large outbreaks of COVID-19 under control and maintained near-elimination status. A key element of epidemic response is the tracking of disease transmissibility in near real-time. During major outbreaks, the effective reproduction number can be estimated from a time-series of case, hospitalisation or death counts. In low or zero incidence settings, knowing the potential for the virus to spread is a response priority. Absence of case data means that this potential cannot be estimated directly. We present a semi-mechanistic modelling framework that draws on time-series of both behavioural data and case data (when disease activity is present) to estimate the transmissibility of SARS-CoV-2 from periods of high to low - or zero - case incidence, with a coherent transition in interpretation across the changing epidemiological situations. Of note, during periods of epidemic activity, our analysis recovers the effective reproduction number, while during periods of low - or zero - case incidence, it provides an estimate of transmission risk. This enables tracking and planning of progress towards the control of large outbreaks, maintenance of virus suppression, and monitoring the risk posed by re-introduction of the virus. We demonstrate the value of our methods by reporting on their use throughout 2020 in Australia, where they have become a central component of the national COVID-19 response.

Using digital traces to build prospective and real-time county-level early warning systems to anticipate COVID-19 outbreaks in the United States

Coronavirus disease 2019 (COVID-19) continues to affect the world, and the design of strategies to curb disease outbreaks requires close monitoring of their trajectories. We present machine learning methods that leverage internet-based digital traces to anticipate sharp increases in COVID-19 activity in U.S. counties. In a complementary direction to the efforts led by the Centers for Disease Control and Prevention (CDC), our models are designed to detect the time when an uptrend in COVID-19 activity will occur. Motivated by the need for finer spatial resolution epidemiological insights, we build upon previous efforts conceived at the state level. Our methods-tested in an out-of-sample manner, as events were unfolding, in 97 counties representative of multiple population sizes across the United States-frequently anticipated increases in COVID-19 activity 1 to 6 weeks before local outbreaks, defined when the effective reproduction number R_t becomes larger than 1 for a period of 2 weeks.

An approximate Bayesian approach for estimation of the instantaneous reproduction number under misreported epidemic data

In epidemic models, the effective reproduction number is of central importance to assess the transmission dynamics of an infectious disease and to orient health intervention strategies. Publicly shared data during an outbreak often suffers from two sources of misreporting (underreporting and delay in reporting) that should not be overlooked when estimating epidemiological parameters. The main statistical challenge in models that intrinsically account for a misreporting process lies in the joint estimation of the time-varying reproduction number and the delay/underreporting parameters. Existing Bayesian approaches typically rely on Markov chain Monte Carlo algorithms that are extremely costly from a computational perspective. We propose a much faster alternative based on Laplacian-P-splines (LPS) that combines Bayesian penalized B-splines for flexible and smooth estimation of the instantaneous reproduction number and Laplace approximations to selected posterior distributions for fast computation. Assuming a known generation interval distribution, the incidence at a given calendar time is governed by the epidemic renewal equation and the delay structure is specified through a composite link framework. Laplace approximations to the conditional posterior of the spline vector are obtained from analytical versions of the gradient and Hessian of the log-likelihood, implying a drastic speed-up in the computation of posterior estimates. Furthermore, the proposed LPS approach can be used to obtain point estimates and approximate credible intervals for the delay and reporting probabilities. Simulation of epidemics with different combinations for the underreporting rate and delay structure (one-day, two-day, and weekend delays) show that the proposed LPS methodology delivers fast and accurate estimates outperforming existing methods that do not take into account underreporting and delay patterns. Finally, LPS is illustrated in two real case studies of epidemic outbreaks.

Community Mitigation Strategies, Mobility, and COVID-19 Incidence Across Three Waves in the United States in 2020

BACKGROUND

Summarizing the impact of community-based mitigation strategies and mobility on COVID-19 infections throughout the pandemic is critical for informing responses and future infectious disease outbreaks. Here, we employed time-series analyses to empirically investigate the relationships between mitigation strategies and mobility on COVID-19 incident cases across US states during the first three waves of infections.

METHODS

We linked data on daily COVID-19 incidence by US state from March to December 2020 with the stringency index, a well-known index capturing the strictness of mitigation strategies, and the trip ratio, which measures the ratio of the number of trips taken per day compared with the same day in 2019. We utilized multilevel models to determine the relative impacts of policy stringency and the trip ratio on COVID-19 cumulative incidence and the effective reproduction number. We stratified analyses by three waves of infections.

RESULTS

Every five-point increase in the stringency index was associated with 2.89% (95% confidence interval = 1.52, 4.26%) and 5.01% (3.02, 6.95%) reductions in COVID-19 incidence for the first and third waves, respectively. Reducing the number of trips taken by 50% compared with the same time in 2019 was associated with a 16.2% (-0.07, 35.2%) decline in COVID-19 incidence at the state level during the second wave and 19.3% (2.30, 39.0%) during the third wave.

CONCLUSIONS

Mitigation strategies and reductions in mobility are associated with marked health gains through the reduction of COVID-19 infections, but we estimate variable impacts depending on policy stringency and levels of adherence.

Modeling local coronavirus outbreaks

This article presents an overview of methods developed for the modeling and control of local coronavirus outbreaks. The article reviews early transmission dynamics featuring exponential growth in infections, and links this to a renewal epidemic model where the current incidence of infection depends upon the expected value of incidence randomly lagged into the past. This leads directly to simple formulas for the fraction of the population infected in an unmitigated outbreak, and reveals herd immunity as the solution to an optimization problem. The model also leads to direct and easy-to-understand formulas for aligning observable epidemic indicators such as cases, hospitalizations and deaths with the unobservable incidence of infection, and as a byproduct leads to a simple first-order approach for estimating the effective reproduction number R t . The model also leads naturally to direct assessments of the effectiveness of isolation in preventing the spread of infection. This is illustrated with application to repeat asymptomatic screening programs of the sort utilized by universities, sports teams and businesses to prevent the spread of infection.

Shifts in global mobility dictate the synchrony of SARS-CoV-2 epidemic waves

BACKGROUND

Human mobility changed in unprecedented ways during the SARS-CoV-2 pandemic. In March and April 2020, when lockdowns and large travel restrictions began in most countries, global air-travel almost entirely halted (92% decrease in commercial global air travel in the months between February and April 2020). Initial recovery in global air travel started around July 2020 and subsequently nearly tripled between May and July 2021. Here, we aim to establish a preliminary link between global mobility patterns and the synchrony of SARS-CoV-2 epidemic waves across the world.

METHODS

We compare epidemic peaks and human global mobility in two time periods: November 2020 to February 2021 (when just over 70 million passengers travelled) and November 2021 to February 2022 (when more than 200 million passengers travelled). We calculate the time interval during which continental epidemic peaks occurred for both of these time periods, and we calculate the pairwise correlations of epidemic waves between all pairs of countries for the same time periods.

RESULTS

We find that as air travel increases at the end of 2021, epidemic peaks around the world are more synchronous with one another, both globally and regionally. Continental epidemic peaks occur globally within a 20 day interval at the end of 2021 compared with 73 days at the end of 2020, and epidemic waves globally are more correlated with one another at the end of 2021.

CONCLUSIONS

This suggests that the rebound in human mobility dictates the synchrony of global and regional epidemic waves. In line with theoretical work, we show that in a more connected world, epidemic dynamics are more synchronized.

The SARS-CoV-2 Delta (B.1.617.2) variant with spike N501Y mutation in the shadow of Omicron emergence

Circulation of the Omicron variant with the reemergence of the N501Y mutation along with many others in the spike protein has once again stirred the academic community. Interestingly, tracing the genetic diversity of SARS-CoV-2 shed light on a less frequent N501Y + Delta variant which has been in the global circulation for some time before the Omicron appearance. This paper aims to present the molecular characteristics of the SARS-CoV-2 Spike_N501Y + Delta variant detected in Bosnia and Herzegovina. The study was conducted during November and December 2021. All patients were tested using real-time RT-PCR for detection of SARS-CoV-2. A representative number of SARS-CoV-2 positive samples was pre-screened using VirSNiP SARS-CoV-2 Spike N501Y kit. The characterization of the viruses was carried out with Illumina RNA Prep with enrichment and the Respiratory Virus Oligo Panel kit. Among the analyzed sequences, we found two isolates of the Delta variant that differ from their most related clade- GK AY.4.3 in additional mutations N501Y and L54F. In this study, we described the presence of a rare form of Delta variant with Spike_N501Y mutation in the shadow of the Omicron emergence. Despite the set of mutations in the Spike protein, this form of Delta variant does not indicate the large-scale consequences for the general population. Further functional studies of this form could provide more information about its antigenicity and infectivity.

Inferring time-varying generation time, serial interval, and incubation period distributions for COVID-19

The generation time distribution, reflecting the time between successive infections in transmission chains, is a key epidemiological parameter for describing COVID-19 transmission dynamics. However, because exact infection times are rarely known, it is often approximated by the serial interval distribution. This approximation holds under the assumption that infectors and infectees share the same incubation period distribution, which may not always be true. We estimated incubation period and serial interval distributions using 629 transmission pairs reconstructed by investigating 2989 confirmed cases in China in January-February 2020, and developed an inferential framework to estimate the generation time distribution that accounts for variation over time due to changes in epidemiology, sampling biases and public health and social measures. We identified substantial reductions over time in the serial interval and generation time distributions. Our proposed method provides more reliable estimation of the temporal variation in the generation time distribution, improving assessment of transmission dynamics.

Impact of spatiotemporal heterogeneity in COVID-19 disease surveillance on epidemiological parameters and case growth rates

SARS-CoV-2 case data are primary sources for estimating epidemiological parameters and for modelling the dynamics of outbreaks. Understanding biases within case-based data sources used in epidemiological analyses is important as they can detract from the value of these rich datasets. This raises questions of how variations in surveillance can affect the estimation of epidemiological parameters such as the case growth rates. We use standardised line list data of COVID-19 from Argentina, Brazil, Mexico and Colombia to estimate delay distributions of symptom-onset-to-confirmation, -hospitalisation and -death as well as hospitalisation-to-death at high spatial resolutions and throughout time. Using these estimates, we model the biases introduced by the delay from symptom-onset-to-confirmation on national and state level case growth rates (rt) using an adaptation of the Richardson-Lucy deconvolution algorithm. We find significant heterogeneities in the estimation of delay distributions through time and space with delay difference of up to 19 days between epochs at the state level. Further, we find that by changing the spatial scale, estimates of case growth rate can vary by up to 0.13 d^-1. Lastly, we find that states with a high variance and/or mean delay in symptom-onset-to-diagnosis also have the largest difference between the rt estimated from raw and deconvolved case counts at the state level. We highlight the importance of high-resolution case-based data in understanding biases in disease reporting and how these biases can be avoided by adjusting case numbers based on empirical delay distributions. Code and openly accessible data to reproduce analyses presented here are available.

Impact of changes in protective behaviors and out-of-household activities by age on COVID-19 transmission and hospitalization in Chicago, Illinois

PURPOSE

Even with an efficacious vaccine, protective behaviors (social distancing, masking) are essential for preventing COVID-19 transmission and could become even more important if current or future variants evade immunity from vaccines or prior infection.

METHODS

We created an agent-based model representing the Chicago population and conducted experiments to determine the effects of varying adult out-of-household activities (OOHA), school reopening, and protective behaviors across age groups on COVID-19 transmission and hospitalizations.

RESULTS

From September-November 2020, decreasing adult protective behaviors and increasing adult OOHA both substantially impacted COVID-19 outcomes; school reopening had relatively little impact when adult protective behaviors and OOHA were maintained. As of November 1, 2020, a 50% reduction in young adult (age 18-40) protective behaviors resulted in increased latent infection prevalence per 100,000 from 15.93 (IQR 6.18, 36.23) to 40.06 (IQR 14.65, 85.21) and 19.87 (IQR 6.83, 46.83) to 47.74 (IQR 18.89, 118.77) with 15% and 45% school reopening. Increasing adult (age ≥18) OOHA from 65% to 80% of prepandemic levels resulted in increased latent infection prevalence per 100,000 from 35.18 (IQR 13.59, 75.00) to 69.84 (IQR 33.27, 145.89) and 38.17 (IQR 15.84, 91.16) to 80.02 (IQR 30.91, 186.63) with 15% and 45% school reopening. Similar patterns were observed for hospitalizations.

CONCLUSIONS

In areas without widespread vaccination coverage, interventions to maintain adherence to protective behaviors, particularly among younger adults and in out-of-household settings, remain a priority for preventing COVID-19 transmission.

Impact of cross-border-associated cases on the SARS-CoV-2 epidemic in Switzerland during summer 2020 and 2021

During the summers of 2020 and 2021, the number of confirmed cases of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections in Switzerland remained at relatively low levels, but grew steadily over time. It remains unclear to what extent epidemic growth during these periods was a result of the relaxation of local control measures or increased traveling and subsequent importation of cases. A better understanding of the role of cross-border-associated cases (imports) on the local epidemic dynamics will help to inform future surveillance strategies. We analyzed routine surveillance data of confirmed cases of SARS-CoV-2 in Switzerland from 1 June to 30 September 2020 and 2021. We used a stochastic branching process model that accounts for superspreading of SARS-CoV-2 to simulate epidemic trajectories in absence and in presence of imports during summer 2020 and 2021. The Swiss Federal Office of Public Health reported 22,919 and 145,840 confirmed cases of SARS-CoV-2 from 1 June to 30 September 2020 and 2021, respectively. Among cases with known place of exposure, 27% (3,276 of 12,088) and 25% (1,110 of 4,368) reported an exposure abroad in 2020 and 2021, respectively. Without considering the impact of imported cases, the steady growth of confirmed cases during summer periods would be consistent with a value of R_e that is significantly above the critical threshold of 1. In contrast, we estimated R_e at 0.84 (95% credible interval, CrI: 0.78-0.90) in 2020 and 0.82 (95% CrI: 0.74-0.90) in 2021 when imported cases were taken into account, indicating that the local R_e was below the critical threshold of 1 during summer. In Switzerland, cross-border-associated SARS-CoV-2 cases had a considerable impact on the local transmission dynamics and can explain the steady growth of the epidemic during the summers of 2020 and 2021.

Monitoring real-time transmission heterogeneity from incidence data

The transmission heterogeneity of an epidemic is associated with a complex mixture of host, pathogen and environmental factors. And it may indicate superspreading events to reduce the efficiency of population-level control measures and to sustain the epidemic over a larger scale and a longer duration. Methods have been proposed to identify significant transmission heterogeneity in historic epidemics based on several data sources, such as contact history, viral genomes and spatial information, which may not be available, and more importantly ignore the temporal trend of transmission heterogeneity. Here we attempted to establish a convenient method to estimate real-time heterogeneity over an epidemic. Within the branching process framework, we introduced an instant-individualheterogenous infectiousness model to jointly characterize the variation in infectiousness both between individuals and among different times. With this model, we could simultaneously estimate the transmission heterogeneity and the reproduction number from incidence time series. We validated the model with data of both simulated and real outbreaks. Our estimates of the overall and real-time heterogeneities of the six epidemics were consistent with those presented in the literature. Additionally, our model is robust to the ubiquitous bias of under-reporting and misspecification of serial interval. By analyzing recent data from South Africa, we found evidence that the Omicron might be of more significant transmission heterogeneity than Delta. Our model based on incidence data was proved to be reliable in estimating the real-time transmission heterogeneity.

Correlation between times to SARS-CoV-2 symptom onset and secondary transmission undermines epidemic control efforts

Severe acute respiratory coronavirus 2 (SARS-CoV-2) infections have been associated with substantial presymptomatic transmission, which occurs when the generation interval-the time between infection of an individual with a pathogen and transmission of the pathogen to another individual-is shorter than the incubation period-the time between infection and symptom onset. We collected a dataset of 257 SARS-CoV-2 transmission pairs in Japan during 2020 and jointly estimated the mean incubation period of infectors (4.8 days, 95 % CrI: 4.4-5.1 days), mean generation interval to when they infect others (4.3 days, 95 % credible interval [CrI]: 4.0-4.7 days), and the correlation (Kendall's tau: 0.5, 95 % CrI: 0.4-0.6) between these two epidemiological parameters. Our finding of a positive correlation and mean generation interval shorter than the mean infector incubation period indicates ample infectiousness before symptom onset and suggests that reliance on isolation of symptomatic COVID-19 cases as a focal point of control efforts is insufficient to address the challenges posed by SARS-CoV-2 transmission dynamics.

Using mechanistic model-based inference to understand and project epidemic dynamics with time-varying contact and vaccination rates

Epidemiological models range in complexity from relatively simple statistical models that make minimal assumptions about the variables driving epidemic dynamics to more mechanistic models that include effects such as vaccine-derived and infection-derived immunity, population structure and heterogeneity. The former are often fitted to data in real-time and used for short-term forecasting, while the latter are more suitable for comparing longer-term scenarios under differing assumptions about control measures or other factors. Here, we present a mechanistic model of intermediate complexity that can be fitted to data in real-time but is also suitable for investigating longer-term dynamics. Our approach provides a bridge between primarily empirical approaches to forecasting and assumption-driven scenario models. The model was developed as a policy advice tool for New Zealand's 2021 outbreak of the Delta variant of SARS-CoV-2 and includes the effects of age structure, non-pharmaceutical interventions, and the ongoing vaccine rollout occurring during the time period studied. We use an approximate Bayesian computation approach to infer the time-varying transmission coefficient from real-time data on reported cases. We then compare projections of the model with future, out-of-sample data. We find that this approach produces a good fit with in-sample data and reasonable forward projections given the inherent limitations of predicting epidemic dynamics during periods of rapidly changing policy and behaviour. Results from the model helped inform the New Zealand Government's policy response throughout the outbreak.

Epidemiology and Transmission Dynamics of Infectious Diseases and Control Measures

The epidemiology and transmission dynamics of infectious diseases must be understood at the individual and community levels to improve public health decision-making for real-time and integrated community-based control strategies. Herein, we explore the epidemiological characteristics for assessing the impact of public health interventions in the community setting and their applications. Computational statistical methods could advance research on infectious disease epidemiology and accumulate scientific evidence of the potential impacts of pharmaceutical/nonpharmaceutical measures to mitigate or control infectious diseases in the community. Novel public health threats from emerging zoonotic infectious diseases are urgent issues. Given these direct and indirect mitigating impacts at various levels to different infectious diseases and their burdens, we must consider an integrated assessment approach, 'One Health', to understand the dynamics and control of infectious diseases.

Late Surges in COVID-19 Cases and Varying Transmission Potential Partially Due to Public Health Policy Changes in 5 Western States, March 10, 2020, to January 10, 2021

OBJECTIVE

This study investigates the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission potential in North Dakota, South Dakota, Montana, Wyoming, and Idaho from March 2020 through January 2021.

METHODS

Time-varying reproduction numbers, R _t , of a 7-d-sliding-window and of non-overlapping-windows between policy changes were estimated using the instantaneous reproduction number method. Linear regression was performed to evaluate if per-capita cumulative case-count varied across counties with different population size or density.

RESULTS

The median 7-d-sliding-window R _t estimates across the studied region varied between 1 and 1.25 during September through November 2020. Between November 13 and 18, R _t was reduced by 14.71% (95% credible interval, CrI, [14.41%, 14.99%]) in North Dakota following a mask mandate; Idaho saw a 1.93% (95% CrI [1.87%, 1.99%]) reduction and Montana saw a 9.63% (95% CrI [9.26%, 9.98%]) reduction following the tightening of restrictions. High-population and high-density counties had higher per-capita cumulative case-count in North Dakota on June 30, August 31, October 31, and December 31, 2020. In Idaho, North Dakota, South Dakota, and Wyoming, there were positive correlations between population size and per-capita weekly incident case-count, adjusted for calendar time and social vulnerability index variables.

CONCLUSIONS

R _t decreased after mask mandate during the region's case-count spike suggested reduction in SARS-CoV-2 transmission.

Forecasting COVID-19 cases by assessing control-intervention effects in Republic of Korea: A statistical modeling approach

The Coronavirus disease of 2019 (COVID-19) is an ongoing public health concern worldwide. COVID-19 infections continue to occur and thus, it is important to assess the effects of various public health measures. This study aims to forecast COVID-19 cases by geographical area in Korea, based on the effects of different control-intervention intensities (CII). Methods involved estimating the effective reproduction number (Rt) by Korean geographical area using the SEIHR model, and the instantaneous reproduction number using statistical model, comparing the epidemic curves and high-, intermediate-, and low-intensity control interventions. Here, short-term four-week forecasts by geographical area were conducted. The mean of delayed instantaneous reproduction number was estimated at 1.36, 1.03, and 0.93 for the low-, intermediate-, and high-intensity control interventions, respectively, in the capital area of Korea from July 16, 2020, to March 4, 2021. The COVID-19 cases were forecasted with an accuracy rate of 11.28%, 13.62%, and 20.19% MAPE in Korea, including both the capital and non-capital areas. High-intensity control measures significantly reduced the reproduction number to be less than one. The proposed model forecasted COVID-19 transmission dynamics with good accuracy and interpretability. High-intensity control intervention, active case detection, and isolation efforts should be maintained to control the pandemic.

A Bayesian predictive analytics model for improving long range epidemic forecasting during an infection wave

Following the outbreak of the coronavirus epidemic in early 2020, municipalities, regional governments and policymakers worldwide had to plan their Non-Pharmaceutical Interventions (NPIs) amidst a scenario of great uncertainty. At this early stage of an epidemic, where no vaccine or medical treatment is in sight, algorithmic prediction can become a powerful tool to inform local policymaking. However, when we replicated one prominent epidemiological model to inform health authorities in a region in the south of Brazil, we found that this model relied too heavily on manually predetermined covariates and was too reactive to changes in data trends. Our four proposed models access data of both daily reported deaths and infections as well as take into account missing data (e.g., the under-reporting of cases) more explicitly, with two of the proposed versions also attempting to model the delay in test reporting. We simulated weekly forecasting of deaths from the period from 31/05/2020 until 31/01/2021, with first week data being used as a cold-start to the algorithm, after which we use a lighter variant of the model for faster forecasting. Because our models are significantly more proactive in identifying trend changes, this has improved forecasting, especially in long-range predictions and after the peak of an infection wave, as they were quicker to adapt to scenarios after these peaks in reported deaths. Assuming reported cases were under-reported greatly benefited the model in its stability, and modelling retroactively-added data (due to the "hot" nature of the data used) had a negligible impact on performance.

Estimation of reproduction numbers in real time: Conceptual and statistical challenges

The reproduction numberR has been a central metric of the COVID-19 pandemic response, published weekly by the UK government and regularly reported in the media. Here, we provide a formal definition and discuss the advantages and most common misconceptions around this quantity. We consider the intuition behind different formulations ofR , the complexities in its estimation (including the unavoidable lags involved), and its value compared to other indicators (e.g. the growth rate) that can be directly observed from aggregate surveillance data and react more promptly to changes in epidemic trend. As models become more sophisticated, with age and/or spatial structure, formulatingR becomes increasingly complicated and inevitably model-dependent. We present some models currently used in the UK pandemic response as examples. Ultimately, limitations in the available data streams, data quality and time constraints force pragmatic choices to be made on a quantity that is an average across time, space, social structure and settings. Effectively communicating these challenges is important but often difficult in an emergency.

Assessing the effect of school closures on the spread of COVID-19 in Zurich

The effect of school closure on the spread of COVID-19 has been discussed intensively in the literature and the news. To capture the interdependencies between children and adults, we consider daily age-stratified incidence data and contact patterns between age groups which change over time to reflect social distancing policy indicators. We fit a multivariate time-series endemic-epidemic model to such data from the Canton of Zurich, Switzerland and use the model to predict the age-specific incidence in a counterfactual approach (with and without school closures). The results indicate a 17% median increase of incidence in the youngest age group (0-14 year olds), whereas the relative increase in the other age groups drops to values between 2% and 3%. We argue that our approach is more informative to policy makers than summarising the effect of school closures with time-dependent effective reproduction numbers, which are difficult to estimate due to the sparsity of incidence counts within the relevant age groups.

Real-time estimation of the effective reproduction number of SARS-CoV-2 in Aotearoa New Zealand

During an epidemic, real-time estimation of the effective reproduction number supports decision makers to introduce timely and effective public health measures. We estimate the time-varying effective reproduction number, R_t , during Aotearoa New Zealand's August 2021 outbreak of the Delta variant of SARS-CoV-2, by fitting the publicly available EpiNow2 model to New Zealand case data. While we do not explicitly model non-pharmaceutical interventions or vaccination coverage, these two factors were the leading drivers of variation in transmission in this period and we describe how changes in these factors coincided with changes in R_t . Alert Level 4, New Zealand's most stringent restriction setting which includes stay-at-home measures, was initially effective at reducing the median R_t to 0.6 (90% CrI 0.4, 0.8) on 29 August 2021. As New Zealand eased certain restrictions and switched from an elimination strategy to a suppression strategy, R_t subsequently increased to a median 1.3 (1.2, 1.4). Increasing vaccination coverage along with regional restrictions were eventually sufficient to reduce R_t below 1. The outbreak peaked at an estimated 198 (172, 229) new infected cases on 10 November, after which cases declined until January 2022. We continue to update R_t estimates in real time as new case data become available to inform New Zealand's ongoing pandemic response.

EpiLPS: A fast and flexible Bayesian tool for estimation of the time-varying reproduction number

In infectious disease epidemiology, the instantaneous reproduction number [Formula: see text] is a time-varying parameter defined as the average number of secondary infections generated by an infected individual at time t. It is therefore a crucial epidemiological statistic that assists public health decision makers in the management of an epidemic. We present a new Bayesian tool (EpiLPS) for robust estimation of the time-varying reproduction number. The proposed methodology smooths the epidemic curve and allows to obtain (approximate) point estimates and credible intervals of [Formula: see text] by employing the renewal equation, using Bayesian P-splines coupled with Laplace approximations of the conditional posterior of the spline vector. Two alternative approaches for inference are presented: (1) an approach based on a maximum a posteriori argument for the model hyperparameters, delivering estimates of [Formula: see text] in only a few seconds; and (2) an approach based on a Markov chain Monte Carlo (MCMC) scheme with underlying Langevin dynamics for efficient sampling of the posterior target distribution. Case counts per unit of time are assumed to follow a negative binomial distribution to account for potential overdispersion in the data that would not be captured by a classic Poisson model. Furthermore, after smoothing the epidemic curve, a "plug-in'' estimate of the reproduction number can be obtained from the renewal equation yielding a closed form expression of [Formula: see text] as a function of the spline parameters. The approach is extremely fast and free of arbitrary smoothing assumptions. EpiLPS is applied on data of SARS-CoV-1 in Hong-Kong (2003), influenza A H1N1 (2009) in the USA and on the SARS-CoV-2 pandemic (2020-2021) for Belgium, Portugal, Denmark and France.

Estimation of local time-varying reproduction numbers in noisy surveillance data

A valuable metric in understanding local infectious disease dynamics is the local time-varying reproduction number, i.e. the expected number of secondary local cases caused by each infected individual. Accurate estimation of this quantity requires distinguishing cases arising from local transmission from those imported from elsewhere. Realistically, we can expect identification of cases as local or imported to be imperfect. We study the propagation of such errors in estimation of the local time-varying reproduction number. In addition, we propose a Bayesian framework for estimation of the true local time-varying reproduction number when identification errors exist. And we illustrate the practical performance of our estimator through simulation studies and with outbreaks of COVID-19 in Hong Kong and Victoria, Australia. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Estimating SARS-CoV-2 variant fitness and the impact of interventions in England using statistical and geo-spatial agent-based models

The SARS-CoV-2 epidemic has been extended by the evolution of more transmissible viral variants. In autumn 2020, the B.1.177 lineage became the dominant variant in England, before being replaced by the B.1.1.7 (Alpha) lineage in late 2020, with the sweep occurring at different times in each region. This period coincided with a large number of non-pharmaceutical interventions (e.g. lockdowns) to control the epidemic, making it difficult to estimate the relative transmissibility of variants. In this paper, we model the spatial spread of these variants in England using a meta-population agent-based model which correctly characterizes the regional variation in cases and distribution of variants. As a test of robustness, we additionally estimated the relative transmissibility of multiple variants using a statistical model based on the renewal equation, which simultaneously estimates the effective reproduction number R. Relative to earlier variants, the transmissibility of B.1.177 is estimated to have increased by 1.14 (1.12-1.16) and that of Alpha by 1.71 (1.65-1.77). The vaccination programme starting in December 2020 is also modelled. Counterfactual simulations demonstrate that the vaccination programme was essential for reopening in March 2021, and that if the January lockdown had started one month earlier, up to 30 k (24 k-38 k) deaths could have been prevented. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Heterogeneity in the onwards transmission risk between local and imported cases affects practical estimates of the time-dependent reproduction number

During infectious disease outbreaks, inference of summary statistics characterizing transmission is essential for planning interventions. An important metric is the time-dependent reproduction number (Rt), which represents the expected number of secondary cases generated by each infected individual over the course of their infectious period. The value of Rt varies during an outbreak due to factors such as varying population immunity and changes to interventions, including those that affect individuals' contact networks. While it is possible to estimate a single population-wide Rt, this may belie differences in transmission between subgroups within the population. Here, we explore the effects of this heterogeneity on Rt estimates. Specifically, we consider two groups of infected hosts: those infected outside the local population (imported cases), and those infected locally (local cases). We use a Bayesian approach to estimate Rt, made available for others to use via an online tool, that accounts for differences in the onwards transmission risk from individuals in these groups. Using COVID-19 data from different regions worldwide, we show that different assumptions about the relative transmission risk between imported and local cases affect Rt estimates significantly, with implications for interventions. This highlights the need to collect data during outbreaks describing heterogeneities in transmission between different infected hosts, and to account for these heterogeneities in methods used to estimate Rt. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Estimating SARS-CoV-2 variant fitness and the impact of interventions in England using statistical and geo-spatial agent-based models

The SARS-CoV-2 epidemic has been extended by the evolution of more transmissible viral variants. In autumn 2020, the B.1.177 lineage became the dominant variant in England, before being replaced by the B.1.1.7 (Alpha) lineage in late 2020, with the sweep occurring at different times in each region. This period coincided with a large number of non-pharmaceutical interventions (e.g. lockdowns) to control the epidemic, making it difficult to estimate the relative transmissibility of variants. In this paper, we model the spatial spread of these variants in England using a meta-population agent-based model which correctly characterizes the regional variation in cases and distribution of variants. As a test of robustness, we additionally estimated the relative transmissibility of multiple variants using a statistical model based on the renewal equation, which simultaneously estimates the effective reproduction number R. Relative to earlier variants, the transmissibility of B.1.177 is estimated to have increased by 1.14 (1.12-1.16) and that of Alpha by 1.71 (1.65-1.77). The vaccination programme starting in December 2020 is also modelled. Counterfactual simulations demonstrate that the vaccination programme was essential for reopening in March 2021, and that if the January lockdown had started one month earlier, up to 30 k (24 k-38 k) deaths could have been prevented. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Data-driven approach in a compartmental epidemic model to assess undocumented infections

Nowcasting and forecasting of epidemic spreading rely on incidence series of reported cases to derive the fundamental epidemiological parameters for a given pathogen. Two relevant drawbacks for predictions are the unknown fractions of undocumented cases and levels of nonpharmacological interventions, which span highly heterogeneously across different places and times. We describe a simple data-driven approach using a compartmental model including asymptomatic and pre-symptomatic contagions that allows to estimate both the level of undocumented infections and the value of effective reproductive number R t from time series of reported cases, deaths, and epidemiological parameters. The method was applied to epidemic series for COVID-19 across different municipalities in Brazil allowing to estimate the heterogeneity level of under-reporting across different places. The reproductive number derived within the current framework is little sensitive to both diagnosis and infection rates during the asymptomatic states. The methods described here can be extended to more general cases if data is available and adapted to other epidemiological approaches and surveillance data.

Assessing epidemic curves for evidence of superspreading

The expected number of secondary infections arising from each index case, referred to as the reproduction or R number, is a vital summary statistic for understanding and managing epidemic diseases. There are many methods for estimating R ; however, few explicitly model heterogeneous disease reproduction, which gives rise to superspreading within the population. We propose a parsimonious discrete-time branching process model for epidemic curves that incorporates heterogeneous individual reproduction numbers. Our Bayesian approach to inference illustrates that this heterogeneity results in less certainty on estimates of the time-varying cohort reproduction number R t . We apply these methods to a COVID-19 epidemic curve for the Republic of Ireland and find support for heterogeneous disease reproduction. Our analysis allows us to estimate the expected proportion of secondary infections attributable to the most infectious proportion of the population. For example, we estimate that the 20% most infectious index cases account for approximately 75%-98% of the expected secondary infections with 95% posterior probability. In addition, we highlight that heterogeneity is a vital consideration when estimating R t .

A simulation-deep reinforcement learning (SiRL) approach for epidemic control optimization

In this paper, we address the controversies of epidemic control planning by developing a novel Simulation-Deep Reinforcement Learning (SiRL) model. COVID-19 reminded constituents over the world that government decision-making could change their lives. During the COVID-19 pandemic, governments were concerned with reducing fatalities as the virus spread but at the same time also maintaining a flowing economy. In this paper, we address epidemic decision-making regarding the interventions necessary given of the epidemic based on the purpose of the decision-maker. Further, we intend to compare different vaccination strategies, such as age-based and random vaccination, to shine a light on who should get priority in the vaccination process. To address these issues, we propose a simulation-deep reinforcement learning (DRL) framework. This framework is composed of an agent-based simulation model and a governor DRL agent that can enforce interventions in the agent-based simulation environment. Computational results show that our DRL agent can learn effective strategies and suggest optimal actions given a specific epidemic situation based on a multi-objective reward structure. We compare our DRL agent's decisions to government interventions at different periods of time during the COVID-19 pandemic. Our results suggest that more could have been done to control the epidemic. In addition, if a random vaccination strategy that allows super-spreaders to get vaccinated early were used, infections would have been reduced by 32% at the expense of 4% more deaths. We also show that a behavioral change of fully quarantining 10% of the risky individuals and using a random vaccination strategy leads to a reduction of the death toll by 14% and 27% compared to the age-based vaccination strategy that was implemented and the New Jersey reported data, respectively. We have also demonstrated the flexibility of our approach to be applied to other locations by validating and applying our model to the COVID-19 case in the state of Kansas.

Using multiple sampling strategies to estimate SARS-CoV-2 epidemiological parameters from genomic sequencing data

The choice of viral sequences used in genetic and epidemiological analysis is important as it can induce biases that detract from the value of these rich datasets. This raises questions about how a set of sequences should be chosen for analysis. We provide insights on these largely understudied problems using SARS-CoV-2 genomic sequences from Hong Kong, China, and the Amazonas State, Brazil. We consider multiple sampling schemes which were used to estimate Rt and rt as well as related R0 and date of origin parameters. We find that both Rt and rt are sensitive to changes in sampling whilst R0 and the date of origin are relatively robust. Moreover, we find that analysis using unsampled datasets result in the most biased Rt and rt estimates for both our Hong Kong and Amazonas case studies. We highlight that sampling strategy choices may be an influential yet neglected component of sequencing analysis pipelines.

Tracking changes in SARS-CoV-2 transmission with a novel outpatient sentinel surveillance system in Chicago, USA

Public health indicators typically used for COVID-19 surveillance can be biased or lag changing community transmission patterns. In this study, we investigate whether sentinel surveillance of recently symptomatic individuals receiving outpatient diagnostic testing for SARS-CoV-2 could accurately assess the instantaneous reproductive number R(t) and provide early warning of changes in transmission. We use data from community-based diagnostic testing sites in the United States city of Chicago. Patients tested at community-based diagnostic testing sites between September 2020 and June 2021, and reporting symptom onset within four days preceding their test, formed the sentinel population. R(t) calculated from sentinel cases agreed well with R(t) from other indicators. Retrospectively, trends in sentinel cases did not precede trends in COVID-19 hospital admissions by any identifiable lead time. In deployment, sentinel surveillance held an operational recency advantage of nine days over hospital admissions. The promising performance of opportunistic sentinel surveillance suggests that deliberately designed outpatient sentinel surveillance would provide robust early warning of increasing transmission.

Epidemiological model based periodic intervention policies for COVID-19 mitigation in the United Kingdom

As the UK, together with numerous countries in the world, moves towards a new phase of the COVID-19 pandemic, there is a need to be able to predict trends in sufficient time to limit the pressure faced by the National Health Service (NHS) and maintain low hospitalisation levels. In this study, we explore the use of an epidemiological compartmental model to devise a periodic adaptive suppression/intervention policy to alleviate the pressure on the NHS. The proposed model facilitates the understanding of the progression of the specific stages of COVID-19 in communities in the UK including: the susceptible population, the infected population, the hospitalised population, the recovered population, the deceased population, and the vaccinated population. We identify the parameters of the model by relying on past data within the period from 1 October 2020 to 1 June 2021. We use the total number of hospitalised patients and the fraction of those infected who are being admitted to hospital to develop adaptive policies: these modulate the recommended level of social restriction measures and realisable vaccination target adjustments. The analysis over the period 1 October 2020 to 1 June 2021 demonstrates our periodic adaptive policies have the potential to reduce the hospitalisation by 58% on average per month. In a further prospective analysis over the period August 2021 to May 2022, we analyse several future scenarios, characterised by the relaxation of restrictions, the vaccination ineffectiveness and the gradual decay of the vaccination-induced immunity within the population. In addition, we simulate the surge of plausible variants characterised by an higher transmission rate. In such scenarios, we show that our periodic intervention is effective and able to maintain the hospitalisation rate to a manageable level.