Practical considerations for measuring the effective reproductive number, Rt

Estimating the effective reproduction number for heterogeneous models using incidence data

The effective reproduction number, R ( t ) , plays a key role in the study of infectious diseases, indicating the current average number of new infections caused by an infected individual in an epidemic process. Estimation methods for the time evolution of R ( t ) , using incidence data, rely on the generation interval distribution, g(τ), which is usually obtained from empirical data or theoretical studies using simple epidemic models. However, for systems that present heterogeneity, either on the host population or in the expression of the disease, there is a lack of data and of a suitable general methodology to obtain g(τ). In this work, we use mathematical models to bridge this gap. We present a general methodology for obtaining explicit expressions of the reproduction numbers and the generation interval distributions, within and between model sub-compartments provided by an arbitrary compartmental model. Additionally, we present the appropriate expressions to evaluate those reproduction numbers using incidence data. To highlight the relevance of such methodology, we apply it to the spread of COVID-19 in municipalities of the state of Rio de Janeiro, Brazil. Using two meta-population models, we estimate the reproduction numbers and the contributions of each municipality in the generation of cases in all others.

Estimating the effective reproduction number for heterogeneous models using incidence data

The effective reproduction number, R ( t ) , plays a key role in the study of infectious diseases, indicating the current average number of new infections caused by an infected individual in an epidemic process. Estimation methods for the time evolution of R ( t ) , using incidence data, rely on the generation interval distribution, g(τ), which is usually obtained from empirical data or theoretical studies using simple epidemic models. However, for systems that present heterogeneity, either on the host population or in the expression of the disease, there is a lack of data and of a suitable general methodology to obtain g(τ). In this work, we use mathematical models to bridge this gap. We present a general methodology for obtaining explicit expressions of the reproduction numbers and the generation interval distributions, within and between model sub-compartments provided by an arbitrary compartmental model. Additionally, we present the appropriate expressions to evaluate those reproduction numbers using incidence data. To highlight the relevance of such methodology, we apply it to the spread of COVID-19 in municipalities of the state of Rio de Janeiro, Brazil. Using two meta-population models, we estimate the reproduction numbers and the contributions of each municipality in the generation of cases in all others.

Commentary on the use of the reproduction number R during the COVID-19 pandemic

Since the beginning of the COVID-19 pandemic, the reproduction number [Formula: see text] has become a popular epidemiological metric used to communicate the state of the epidemic. At its most basic, [Formula: see text] is defined as the average number of secondary infections caused by one primary infected individual. [Formula: see text] seems convenient, because the epidemic is expanding if [Formula: see text] and contracting if [Formula: see text]. The magnitude of [Formula: see text] indicates by how much transmission needs to be reduced to control the epidemic. Using [Formula: see text] in a naïve way can cause new problems. The reasons for this are threefold: (1) There is not just one definition of [Formula: see text] but many, and the precise definition of [Formula: see text] affects both its estimated value and how it should be interpreted. (2) Even with a particular clearly defined [Formula: see text], there may be different statistical methods used to estimate its value, and the choice of method will affect the estimate. (3) The availability and type of data used to estimate [Formula: see text] vary, and it is not always clear what data should be included in the estimation. In this review, we discuss when [Formula: see text] is useful, when it may be of use but needs to be interpreted with care, and when it may be an inappropriate indicator of the progress of the epidemic. We also argue that careful definition of [Formula: see text], and the data and methods used to estimate it, can make [Formula: see text] a more useful metric for future management of the epidemic.

The Effect of Strict Lockdown on Omicron SARS-CoV-2 Variant Transmission in Shanghai

Omicron, the current SARS-CoV-2 variant of concern, is much more contagious than other previous variants. Whether strict lockdown could effectively curb the transmission of Omicron is largely unknown. In this retrospective study, we compared the strictness of government lockdown policies in Shanghai and other countries. Based on the daily Omicron case number from 1 March 2022 to 30 April 2022, the effective reproductive numbers in this Shanghai Omicron wave were calculated to confirm the impact of strict lockdown on Omicron transmission. Pearson correlation was conducted to illustrate the determining factor of strict lockdown outcomes in the 16 different districts of Shanghai. After a very strict citywide lockdown since April 1st, the average daily effective reproductive number reduced significantly, indicating that strict lockdown could slow down the spreading of Omicron. Omicron control is more challenging in districts with higher population mobility and lockdown is more likely to decrease the number of asymptomatic carriers than the symptomatic cases. All these findings indicate that the strict lockdown could curb the transmission of Omicron effectively, especially for the asymptomatic spread, and suggest that differentiated COVID-19 prevention and control measures should be adopted according to the population density and demographic composition of each community.

Estimation and worldwide monitoring of the effective reproductive number of SARS-CoV-2

The effective reproductive number R_e is a key indicator of the growth of an epidemic. Since the start of the SARS-CoV-2 pandemic, many methods and online dashboards have sprung up to monitor this number through time. However, these methods are not always thoroughly tested, correctly placed in time, or are overly confident during high incidence periods. Here, we present a method for timely estimation of R_e, applied to COVID-19 epidemic data from 170 countries. We thoroughly evaluate the method on simulated data, and present an intuitive web interface for interactive data exploration. We show that, in early 2020, in the majority of countries the estimated R_e dropped below 1 only after the introduction of major non-pharmaceutical interventions. For Europe the implementation of non-pharmaceutical interventions was broadly associated with reductions in the estimated R_e. Globally though, relaxing non-pharmaceutical interventions had more varied effects on subsequent R_e estimates. Our framework is useful to inform governments and the general public on the status of epidemics in their country, and is used as the official source of R_e estimates for SARS-CoV-2 in Switzerland. It further allows detailed comparison between countries and in relation to covariates such as implemented public health policies, mobility, behaviour, or weather data.

Estimation and worldwide monitoring of the effective reproductive number of SARS-CoV-2

The effective reproductive number R_e is a key indicator of the growth of an epidemic. Since the start of the SARS-CoV-2 pandemic, many methods and online dashboards have sprung up to monitor this number through time. However, these methods are not always thoroughly tested, correctly placed in time, or are overly confident during high incidence periods. Here, we present a method for timely estimation of R_e, applied to COVID-19 epidemic data from 170 countries. We thoroughly evaluate the method on simulated data, and present an intuitive web interface for interactive data exploration. We show that, in early 2020, in the majority of countries the estimated R_e dropped below 1 only after the introduction of major non-pharmaceutical interventions. For Europe the implementation of non-pharmaceutical interventions was broadly associated with reductions in the estimated R_e. Globally though, relaxing non-pharmaceutical interventions had more varied effects on subsequent R_e estimates. Our framework is useful to inform governments and the general public on the status of epidemics in their country, and is used as the official source of R_e estimates for SARS-CoV-2 in Switzerland. It further allows detailed comparison between countries and in relation to covariates such as implemented public health policies, mobility, behaviour, or weather data.

Over the past two and a half years, countries around the globe have struggled to control the transmission of the SARS-CoV-2 virus within their borders. To manage the situation, it is important to have an accurate picture of how fast the virus is spreading. This can be achieved by calculating the effective reproductive number (Re), which describes how many people, on average, someone with COVID-19 is likely to infect. If the Re is greater than one, the virus is infecting increasingly more people, but if it is smaller than one, the number of cases is declining.

Scientists use various strategies to estimate the Re, which each have their own strengths and weaknesses. One of the main difficulties is that infections are typically recorded only when people test positive for COVID-19, are hospitalized with the virus, or die. This means that the data provides a delayed representation of when infections are happening. Furthermore, changes in these records occur later than measures that change the infection dynamics. As a result, researchers need to take these delays into account when estimating Re.

Here, Huisman, Scire et al. have developed a new method for estimating the Re based on available data records, statistically taking into account the above-mentioned delays. An online dashboard with daily updates was then created so that policy makers and the population could monitor the values over time.

For over two years, Huisman, Scire et al. have been applying their tool and dashboard to COVID-19 data from 170 countries. They found that public health interventions, such as mask requirements and lockdowns, did help reduce the Re in Europe. But the effects were not uniform across the globe, likely because of variations in how restrictions were implemented and followed during the pandemic. In early 2020, the Re only dropped below one after countries put lockdowns or other severe measures in place.

The Re values added to the dashboard over the last two years have been used pro-actively to inform public health policies in Switzerland and to monitor the spread of SARS-CoV-2 in South Africa. The team has also recently released programming software based on this method that can be used to track future disease outbreaks, and extended the method to estimate the Re using SARS-CoV-2 levels in wastewater.

SARS-CoV-2 Transmission Potential and Policy Changes in South Carolina, February 2020 - January 2021

INTRODUCTION

We aimed to examine how public health policies influenced the dynamics of coronavirus disease 2019 (COVID-19) time-varying reproductive number (R _t ) in South Carolina from February 26, 2020, to January 1, 2021.

METHODS

COVID-19 case series (March 6, 2020, to January 10, 2021) were shifted by 9 d to approximate the infection date. We analyzed the effects of state and county policies on R _t using EpiEstim. We performed linear regression to evaluate if per-capita cumulative case count varies across counties with different population size.

RESULTS

R _t shifted from 2-3 in March to <1 during April and May. R _t rose over the summer and stayed between 1.4 and 0.7. The introduction of statewide mask mandates was associated with a decline in R _t (-15.3%; 95% CrI, -13.6%, -16.8%), and school re-opening, an increase by 12.3% (95% CrI, 10.1%, 14.4%). Less densely populated counties had higher attack rates (P < 0.0001).

CONCLUSIONS

The R _t dynamics over time indicated that public health interventions substantially slowed COVID-19 transmission in South Carolina, while their relaxation may have promoted further transmission. Policies encouraging people to stay home, such as closing nonessential businesses, were associated with R _t reduction, while policies that encouraged more movement, such as re-opening schools, were associated with R _t increase.

An assessment of transmission dynamics via time-varying reproduction number of the second wave of the COVID-19 epidemic in Fiji

This study involves the estimation of a key epidemiological parameter for evaluating and monitoring the transmissibility of a disease. The time-varying reproduction number is the index for quantifying the transmissibility of infectious diseases. Accurate and timely estimation of the time-varying reproduction number is essential for optimizing non-pharmacological interventions and movement control orders during epidemics. The time-varying reproduction number for the second wave of the pandemic in Fiji is estimated using the popular EpiEstim R package and the publicly available COVID-19 data from 19 April 2021 to 1 December 2021. Our findings show that the non-pharmacological interventions and movement control orders introduced and enforced by the Fijian Government had a significant impact in preventing the spread of COVID-19. Moreover, the results show that many restrictions were either relaxed or eased when the time-varying reproduction number was below the threshold value of 1. The results have provided some information on the second wave of the COVID-19 pandemic that could be used in the future as a guide for public health policymakers in Fiji. Estimation of time-varying reproduction numbers would be helpful for continuous monitoring of the effectiveness of the current public health policies that are being implemented in Fiji.

Impact of layered non-pharmacological interventions on COVID-19 transmission dynamics in Yucatan, Mexico

Background

The pandemic propagation of SARS-CoV-2 led to the adoption of a myriad of non-pharmacological interventions (NPIs, e.g., social distancing, mobility restrictions, gathering restrictions) in the Americas. Using national epidemiological data, here we report the impact of the layered adoption of multiple NPIs aimed at curving SARS-CoV-2 transmission in Yucatan State, Mexico.

Methods

Data from suspected and laboratory confirmed COVID-19 cases during 2020 were analyzed by age groups and sex, clinical signs, and symptoms as well as outcome. The impact of NPIs was quantified using time-varying reproduction numbers (R t) estimated as a time-series and by sectors of the city.

Findings

A total of 69,602 suspected cases were reported, 39.3% were laboratory-confirmed. Men were hospitalized (60.2%), more severely ill (3% vs 1.9%) and more likely to die (62%) than women. Early in the outbreak, all sectors in Merida hadR t estimates above unity. Once all NPÍs were in place,R t values were dramatically reduced below one, and in the last interval transmission estimates ofR t remained below one in all sectors.

Interpretation

In the absence of a COVID-19 vaccination program, the combination and wide adherence of NPÍs led to a low and stable trend in SARS-CoV-2 transmission that did not overwhelm the health sector. Our study reflects that a controlled and planned ease of restrictions to balance health, social and economic recovery resulted in a single wave of transmission that prolonged at low and stable levels.

Funding

GVP received funding from Emory University via the MP3 Initiative.

The unmitigated profile of COVID-19 infectiousness

Quantifying the temporal dynamics of infectiousness of individuals infected with SARS-CoV-2 is crucial for understanding the spread of COVID-19 and for evaluating the effectiveness of mitigation strategies. Many studies have estimated the infectiousness profile using observed serial intervals. However, statistical and epidemiological biases could lead to underestimation of the duration of infectiousness. We correct for these biases by curating data from the initial outbreak of the pandemic in China (when mitigation was minimal), and find that the infectiousness profile of the original strain is longer than previously thought. Sensitivity analysis shows our results are robust to model structure, assumed growth rate and potential observational biases. Although unmitigated transmission data is lacking for variants of concern (VOCs), previous analyses suggest that the alpha and delta variants have faster within-host kinetics, which we extrapolate to crude estimates of variant-specific unmitigated generation intervals. Knowing the unmitigated infectiousness profile of infected individuals can inform estimates of the effectiveness of isolation and quarantine measures. The framework presented here can help design better quarantine policies in early stages of future epidemics.

Reconstructing the course of the COVID-19 epidemic over 2020 for US states and counties: Results of a Bayesian evidence synthesis model

Reported COVID-19 cases and deaths provide a delayed and incomplete picture of SARS-CoV-2 infections in the United States (US). Accurate estimates of both the timing and magnitude of infections are needed to characterize viral transmission dynamics and better understand COVID-19 disease burden. We estimated time trends in SARS-CoV-2 transmission and other COVID-19 outcomes for every county in the US, from the first reported COVID-19 case in January 13, 2020 through January 1, 2021. To do so we employed a Bayesian modeling approach that explicitly accounts for reporting delays and variation in case ascertainment, and generates daily estimates of incident SARS-CoV-2 infections on the basis of reported COVID-19 cases and deaths. The model is freely available as the covidestim R package. Nationally, we estimated there had been 49 million symptomatic COVID-19 cases and 404,214 COVID-19 deaths by the end of 2020, and that 28% of the US population had been infected. There was county-level variability in the timing and magnitude of incidence, with local epidemiological trends differing substantially from state or regional averages, leading to large differences in the estimated proportion of the population infected by the end of 2020. Our estimates of true COVID-19 related deaths are consistent with independent estimates of excess mortality, and our estimated trends in cumulative incidence of SARS-CoV-2 infection are consistent with trends in seroprevalence estimates from available antibody testing studies. Reconstructing the underlying incidence of SARS-CoV-2 infections across US counties allows for a more granular understanding of disease trends and the potential impact of epidemiological drivers.

Estimating the time-varying reproduction number for COVID-19 in South Africa during the first four waves using multiple measures of incidence for public and private sectors across four waves

Objectives

We aimed to quantify transmission trends in South Africa during the first four waves of the COVID-19 pandemic using estimates of the time-varying reproduction number (R) and to compare the robustness of R estimates based on three different data sources and using data from public and private sector service providers.

Methods

We estimated R from March 2020 through April 2022, nationally and by province, based on time series of rt-PCR-confirmed cases, hospitalizations, and hospital-associated deaths, using a method which models daily incidence as a weighted sum of past incidence. We also estimated R separately using public and private sector data.

Results

Nationally, the maximum case-based R following the introduction of lockdown measures was 1.55 (CI: 1.43-1.66), 1.56 (CI: 1.47-1.64), 1.46 (CI: 1.38-1.53) and 3.33 (CI: 2.84-3.97) during the first (Wuhan-Hu), second (Beta), third (Delta), and fourth (Omicron) waves respectively. Estimates based on the three data sources (cases, hospitalisations, deaths) were generally similar during the first three waves but case-based estimates were higher during the fourth wave. Public and private sector R estimates were generally similar except during the initial lockdowns and in case-based estimates during the fourth wave.

Discussion

Agreement between R estimates using different data sources during the first three waves suggests that data from any of these sources could be used in the early stages of a future pandemic. High R estimates for Omicron relative to earlier waves is interesting given a high level of exposure pre-Omicron. The agreement between public and private sector R estimates highlights the fact that clients of the public and private sectors did not experience two separate epidemics, except perhaps to a limited extent during the strictest lockdowns in the first wave.

Understanding the transmission dynamics of a large-scale measles outbreak in Southern Vietnam

OBJECTIVES

During 2018-2020, Southern Vietnam experienced a large measles outbreak of over 26,000 cases. We aimed to understand and quantify the measles spread in space-time dependence and the transmissibility during the outbreak.

METHODS

Measles surveillance reported cases between 1/2018 and 6/2020, vaccination coverage, and population data at provincial level were used. To illustrate the spatiotemporal pattern of disease spread, we employed the endemic-epidemic multivariate time series model decomposing measles risk additively into autoregressive, spatiotemporal, and endemic component. Likelihood-based estimation procedures were performed to determine the time-varying reproductive number R_e of measles.

RESULTS

Our analysis shows that measles incidence was associated with vaccination coverage heterogeneity and spatial interaction between provincial units. The risk of infections was dominated by between-province transmission (36.1% to 78.8%), followed by local endogenous transmission (4.1% to 61.5%) whereas the endemic behavior had a relatively small contribution (2.1% to 33.4%) across provinces. In the exponential phase of the epidemic, R_e was above the threshold with a maximum value of 2.34 (95%CI: 2.20-2.46).

CONCLUSION

Local vaccination coverage and human mobility are important factors contributing to the measles dynamics in Southern Vietnam and the high risk of inter-provincial transmission is of most concern. Strengthening disease surveillance is recommended, and further research is essential to understand the relative contribution of population immunity and control measures in measles epidemics.

Extended Bayesian endemic–epidemic models to incorporate mobility data into COVID‐19 forecasting

Forecasting the number of daily COVID‐19 cases is critical in the short‐term planning of hospital and other public resources. One potentially important piece of information for forecasting COVID‐19 cases is mobile device location data that measure the amount of time an individual spends at home. Endemic–epidemic (EE) time series models are recently proposed autoregressive models where the current mean case count is modelled as a weighted average of past case counts multiplied by an autoregressive rate, plus an endemic component. We extend EE models to include a distributed‐lag model in order to investigate the association between mobility and the number of reported COVID‐19 cases; we additionally include a weekly first‐order random walk to capture additional temporal variation. Further, we introduce a shifted negative binomial weighting scheme for the past counts that is more flexible than previously proposed weighting schemes. We perform inference under a Bayesian framework to incorporate parameter uncertainty into model forecasts. We illustrate our methods using data from four US counties.

An autonomous compartmental model for accelerating epidemics

In Fall 2020, several European countries reported rapid increases in COVID-19 cases along with growing estimates of the effective reproduction rates. Such an acceleration in epidemic spread is usually attributed to time-dependent effects, e.g. human travel, seasonal behavioral changes, mutations of the pathogen etc. In this case however the acceleration occurred when counter measures such as testing and contact tracing exceeded their capacity limit. Considering Austria as an example, here we show that this dynamics can be captured by a time-independent, i.e. autonomous, compartmental model that incorporates these capacity limits. In this model, the epidemic acceleration coincides with the exhaustion of mitigation efforts, resulting in an increasing fraction of undetected cases that drive the effective reproduction rate progressively higher. We demonstrate that standard models which does not include this effect necessarily result in a systematic underestimation of the effective reproduction rate.

Modeling the Potential Impact of Remdesivir Treatment for Hospitalized Patients with COVID-19 in Saudi Arabia on Healthcare Resource Use and Direct Hospital Costs: A Hypothetical Study

Background and Objectives

Coronavirus disease 2019 (COVID-19) has spread rapidly worldwide. Saudi Arabia was significantly impacted by COVID-19. In March 2021, 381,000 cases were reported with 6539 deaths. This study attempts to quantify the impact of remdesivir on healthcare costs in Saudi Arabia, in terms of intensive care unit admissions, mechanical ventilation, and death prevention.

Methods

A forecasting model was designed to estimate the impact of remdesivir on the capacity of intensive care units and healthcare costs with patients requiring low flow oxygen therapy. The forecasting model was applied in the Saudi context with a 20-week projection between 1 February and 14 June, 2021. Model inputs were collected from published global and Saudi literature, available forecasting resources, and expert opinions. Three scenarios were assumed: the effective pandemic infection rate (Rt) remains at 1, the Rt increases up to 1.2, and the Rt declines from 1 to 0.8 over the study period.

Results

The model estimated that the use of remdesivir in hospitalized patients, in the optimistic and pessimistic scenarios, could prevent between 1520 and 3549 patient transfers to intensive care units and mechanical ventilation, prevent between 815 and 1582 deaths, and make potential cost savings between $US154 million and $US377 million owing to the reduction in intensive care unit capacity, respectively.

Conclusions

The treatment with remdesivir may improve patient outcomes and reduce the burden on healthcare resources during this pandemic.

Supplementary Information

The online version contains supplementary material available at 10.1007/s40261-022-01177-z.

Statistical Deconvolution for Inference of Infection Time Series

Accurate measurement of daily infection incidence is crucial to epidemic response. However, delays in symptom onset, testing, and reporting obscure the dynamics of transmission, necessitating methods to remove the effects of stochastic delays from observed data. Existing estimators can be sensitive to model misspecification and censored observations; many analysts have instead used methods that exhibit strong bias. We develop an estimator with a regularization scheme to cope with stochastic delays, which we term the robust incidence deconvolution estimator. We compare the method to existing estimators in a simulation study, measuring accuracy in a variety of experimental conditions. We then use the method to study COVID-19 records in the United States, highlighting its stability in the face of misspecification and right censoring. To implement the robust incidence deconvolution estimator, we release incidental, a ready-to-use R implementation of our estimator that can aid ongoing efforts to monitor the COVID-19 pandemic.

Inferring the effective reproductive number from deterministic and semi-deterministic compartmental models using incidence and mobility data

The effective reproduction number (ℜt) is a theoretical indicator of the course of an infectious disease that allows policymakers to evaluate whether current or previous control efforts have been successful or whether additional interventions are necessary. This metric, however, cannot be directly observed and must be inferred from available data. One approach to obtaining such estimates is fitting compartmental models to incidence data. We can envision these dynamic models as the ensemble of structures that describe the disease’s natural history and individuals’ behavioural patterns. In the context of the response to the COVID-19 pandemic, the assumption of a constant transmission rate is rendered unrealistic, and it is critical to identify a mathematical formulation that accounts for changes in contact patterns. In this work, we leverage existing approaches to propose three complementary formulations that yield similar estimates for ℜt based on data from Ireland’s first COVID-19 wave. We describe these Data Generating Processes (DGP) in terms of State-Space models. Two (DGP1 and DGP2) correspond to stochastic process models whose transmission rate is modelled as Brownian motion processes (Geometric and Cox-Ingersoll-Ross). These DGPs share a measurement model that accounts for incidence and transmission rates, where mobility data is assumed as a proxy of the transmission rate. We perform inference on these structures using Iterated Filtering and the Particle Filter. The final DGP (DGP3) is built from a pool of deterministic models that describe the transmission rate as information delays. We calibrate this pool of models to incidence reports using Hamiltonian Monte Carlo. By following this complementary approach, we assess the tradeoffs associated with each formulation and reflect on the benefits/risks of incorporating proxy data into the inference process. We anticipate this work will help evaluate the implications of choosing a particular formulation for the dynamics and observation of the time-varying transmission rate.

Inferring the spread of COVID-19: the role of time-varying reporting rate in epidemiological modelling

The role of epidemiological models is crucial for informing public health officials during a public health emergency, such as the COVID-19 pandemic. However, traditional epidemiological models fail to capture the time-varying effects of mitigation strategies and do not account for under-reporting of active cases, thus introducing bias in the estimation of model parameters. To infer more accurate parameter estimates and to reduce the uncertainty of these estimates, we extend the SIR and SEIR epidemiological models with two time-varying parameters that capture the transmission rate and the rate at which active cases are reported to health officials. Using two real data sets of COVID-19 cases, we perform Bayesian inference via our SIR and SEIR models with time-varying transmission and reporting rates and via their standard counterparts with constant rates; our approach provides parameter estimates with more realistic interpretation, and 1-week ahead predictions with reduced uncertainty. Furthermore, we find consistent under-reporting in the number of active cases in the data that we consider, suggesting that the initial phase of the pandemic was more widespread than previously reported.

On the use of the reproduction number for SARS-CoV-2: Estimation, misinterpretations and relationships with other ecological measures

The basic reproduction number, R 0, and its real-time analogue, Rt , are summary measures that reflect the ability of an infectious disease to spread through a population. Estimation methods for Rt  have a long history, have been widely developed and are now enhanced by application to the COVID-19 pandemic. While retrospective analyses of Rt have provided insight into epidemic dynamics and the effects of control strategies in prior outbreaks, misconceptions around the interpretation of Rt have arisen with broader recognition and near real-time monitoring of this parameter alongside reported case data during the COVID-19 pandemic. Here, we discuss some widespread misunderstandings regarding the use of Rt  as a barometer for population risk and its related use as an 'on/off' switch for policy decisions regarding relaxation of non-pharmaceutical interventions. Computation of Rt  from downstream data (e.g. hospitalizations) when infection counts are unreliable exacerbates lags between when transmission happens and when events are recorded. We also discuss analyses that have shown various relationships between Rt  and measures of mobility, vaccination coverage and a test-trace-isolation intervention in different settings.

A direct comparison of methods for assessing the threat from emerging infectious diseases in seasonally varying environments

Seasonal variations in environmental conditions lead to changing infectious disease epidemic risks at different times of year. The probability that early cases initiate a major epidemic depends on the season in which the pathogen enters the population. The instantaneous epidemic risk (IER) can be tracked. This quantity is straightforward to calculate, and corresponds to the probability of a major epidemic starting from a single case introduced at time t=t₀, assuming that environmental conditions remain identical from that time onwards (i.e. for all t≥t₀). However, the threat when a pathogen enters the population in fact depends on changes in environmental conditions occurring within the timescale of the initial phase of the outbreak. For that reason, we compare the IER with a different metric: the case epidemic risk (CER). The CER corresponds to the probability of a major epidemic starting from a single case entering the population at time t=t₀, accounting for changes in environmental conditions after that time. We show how the IER and CER can be calculated using different epidemiological models (the stochastic Susceptible-Infectious-Removed model and a stochastic host-vector model that is parameterised using temperature data for Miami) in which transmission parameters vary temporally. While the IER is always easy to calculate numerically, the adaptable method we provide for calculating the CER for the host-vector model can also be applied easily and solved using widely available software tools. In line with previous research, we demonstrate that if a pathogen is likely to either invade the population or fade out on a fast timescale compared to changes in environmental conditions, the IER closely matches the CER. However, if this is not the case, the IER and the CER can be significantly different, and so the CER should be used. This demonstrates the need to consider future changes in environmental conditions carefully when assessing the risk posed by emerging pathogens.

Biological Properties of SARS-CoV-2 Variants: Epidemiological Impact and Clinical Consequences

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a virus that belongs to the coronavirus family and is the cause of coronavirus disease 2019 (COVID-19). As of May 2022, it had caused more than 500 million infections and more than 6 million deaths worldwide. Several vaccines have been produced and tested over the last two years. The SARS-CoV-2 virus, on the other hand, has mutated over time, resulting in genetic variation in the population of circulating variants during the COVID-19 pandemic. It has also shown immune-evading characteristics, suggesting that vaccinations against these variants could be potentially ineffective. The purpose of this review article is to investigate the key variants of concern (VOCs) and mutations of the virus driving the current pandemic, as well as to explore the transmission rates of SARS-CoV-2 VOCs in relation to epidemiological factors and to compare the virus's transmission rate to that of prior coronaviruses. We examined and provided key information on SARS-CoV-2 VOCs in this study, including their transmissibility, infectivity rate, disease severity, affinity for angiotensin-converting enzyme 2 (ACE2) receptors, viral load, reproduction number, vaccination effectiveness, and vaccine breakthrough.

Mitigation of SARS-CoV-2 transmission at a large public university

In Fall 2020, universities saw extensive transmission of SARS-CoV-2 among their populations, threatening health of the university and surrounding communities, and viability of in-person instruction. Here we report a case study at the University of Illinois at Urbana-Champaign, where a multimodal “SHIELD: Target, Test, and Tell” program, with other non-pharmaceutical interventions, was employed to keep classrooms and laboratories open. The program included epidemiological modeling and surveillance, fast/frequent testing using a novel low-cost and scalable saliva-based RT-qPCR assay for SARS-CoV-2 that bypasses RNA extraction, called covidSHIELD, and digital tools for communication and compliance. In Fall 2020, we performed >1,000,000 covidSHIELD tests, positivity rates remained low, we had zero COVID-19-related hospitalizations or deaths amongst our university community, and mortality in the surrounding Champaign County was reduced more than 4-fold relative to expected. This case study shows that fast/frequent testing and other interventions mitigated transmission of SARS-CoV-2 at a large public university.

Mitigation of SARS-CoV-2 transmission at a large public university

In Fall 2020, universities saw extensive transmission of SARS-CoV-2 among their populations, threatening health of the university and surrounding communities, and viability of in-person instruction. Here we report a case study at the University of Illinois at Urbana-Champaign, where a multimodal “SHIELD: Target, Test, and Tell” program, with other non-pharmaceutical interventions, was employed to keep classrooms and laboratories open. The program included epidemiological modeling and surveillance, fast/frequent testing using a novel low-cost and scalable saliva-based RT-qPCR assay for SARS-CoV-2 that bypasses RNA extraction, called covidSHIELD, and digital tools for communication and compliance. In Fall 2020, we performed >1,000,000 covidSHIELD tests, positivity rates remained low, we had zero COVID-19-related hospitalizations or deaths amongst our university community, and mortality in the surrounding Champaign County was reduced more than 4-fold relative to expected. This case study shows that fast/frequent testing and other interventions mitigated transmission of SARS-CoV-2 at a large public university.

Safely opening university campuses has been a major challenge during the COVID-19 pandemic. Here, the authors describe a program of public health measures employed at a university in the United States which, combined with other non-pharmaceutical interventions, allowed the university to stay open in fall 2020 with limited evidence of transmission.

The importance of the generation interval in investigating dynamics and control of new SARS-CoV-2 variants

Inferring the relative strength (i.e. the ratio of reproduction numbers) and relative speed (i.e. the difference between growth rates) of new SARS-CoV-2 variants is critical to predicting and controlling the course of the current pandemic. Analyses of new variants have primarily focused on characterizing changes in the proportion of new variants, implicitly or explicitly assuming that the relative speed remains fixed over the course of an invasion. We use a generation-interval-based framework to challenge this assumption and illustrate how relative strength and speed change over time under two idealized interventions: a constant-strength intervention like idealized vaccination or social distancing, which reduces transmission rates by a constant proportion, and a constant-speed intervention like idealized contact tracing, which isolates infected individuals at a constant rate. In general, constant-strength interventions change the relative speed of a new variant, while constant-speed interventions change its relative strength. Differences in the generation-interval distributions between variants can exaggerate these changes and modify the effectiveness of interventions. Finally, neglecting differences in generation-interval distributions can bias estimates of relative strength.

Modeling the COVID-19 pandemic: a primer and overview of mathematical epidemiology

Since the start of the still ongoing COVID-19 pandemic, there have been many modeling efforts to assess several issues of importance to public health. In this work, we review the theory behind some important mathematical models that have been used to answer questions raised by the development of the pandemic. We start revisiting the basic properties of simple Kermack-McKendrick type models. Then, we discuss extensions of such models and important epidemiological quantities applied to investigate the role of heterogeneity in disease transmission e.g. mixing functions and superspreading events, the impact of non-pharmaceutical interventions in the control of the pandemic, vaccine deployment, herd-immunity, viral evolution and the possibility of vaccine escape. From the perspective of mathematical epidemiology, we highlight the important properties, findings, and, of course, deficiencies, that all these models have.

Real-time estimation of the epidemic reproduction number: Scoping review of the applications and challenges

The time-varying reproduction number (Rt) is an important measure of transmissibility during outbreaks. Estimating whether and how rapidly an outbreak is growing (Rt > 1) or declining (Rt < 1) can inform the design, monitoring and adjustment of control measures in real-time. We use a popular R package for Rt estimation, EpiEstim, as a case study to evaluate the contexts in which Rt estimation methods have been used and identify unmet needs which would enable broader applicability of these methods in real-time. A scoping review, complemented by a small EpiEstim user survey, highlight issues with the current approaches, including the quality of input incidence data, the inability to account for geographical factors, and other methodological issues. We summarise the methods and software developed to tackle the problems identified, but conclude that significant gaps remain which should be addressed to enable easier, more robust and applicable estimation of Rt during epidemics.

Cold-Season Epidemic Dynamics of COVID-19 in Two Major Metropolitan Areas in Greece: Hypotheses and Implications for Public Health Interventions

Many respiratory viruses, including coronaviruses, follow seasonal transmission dynamics. Analyzing the social and environmental mechanics of the emergence of SARS-CoV-2 over the first cold season provides insight into designing targeted interventions. We analyzed all fully anonymized SARS-CoV-2 case data in two metropolitan areas, Attika and Thessaloniki, diagnosed between September 1st and December 31st, 2020. The emergence of the second wave in Greece occurred in October-November. SARS-CoV-2 diagnoses in Thessaloniki increased quasi-exponentially in mid-October, coinciding with the increase in the proportion of diagnoses in young people aged 18–39. The same pattern was observed in Attika with an almost 2-week delay, even though Attika had a higher prevalence of cases throughout summer until the second wave. Crucially, the nighttime temperature in Thessaloniki dropped below 18°C 3 weeks earlier than that in Attika. Epidemic growth was independently associated with the proportion of cases attributed to the 18–39 age group as well as with the drop in nighttime temperature below 18°C in both metropolitan areas but with a time difference. This pattern can be explained by a shift of nighttime entertainment activities from open-air to closed spaces, which occurs as nighttime temperature drops. Vaccination of young individuals can be crucial in decelerating the cold-season dynamics of SARS-CoV-2.

Wastewater-Based Estimation of the Effective Reproductive Number of SARS-CoV-2

BACKGROUND

The effective reproductive number, R e , is a critical indicator to monitor disease dynamics, inform regional and national policies, and estimate the effectiveness of interventions. It describes the average number of new infections caused by a single infectious person through time. To date, R e estimates are based on clinical data such as observed cases, hospitalizations, and/or deaths. These estimates are temporarily biased when clinical testing or reporting strategies change.

OBJECTIVES

We show that the dynamics of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) RNA in wastewater can be used to estimate R e in near real time, independent of clinical data and without the associated biases.

METHODS

We collected longitudinal measurements of SARS-CoV-2 RNA in wastewater in Zurich, Switzerland, and San Jose, California, USA. We combined this data with information on the temporal dynamics of shedding (the shedding load distribution) to estimate a time series proportional to the daily COVID-19 infection incidence. We estimated a wastewater-based R e from this incidence.

RESULTS

The method to estimate R e from wastewater worked robustly on data from two different countries and two wastewater matrices. The resulting estimates were as similar to the R e estimates from case report data as R e estimates based on observed cases, hospitalizations, and deaths are among each other. We further provide details on the effect of sampling frequency and the shedding load distribution on the ability to infer R e .

DISCUSSION

To our knowledge, this is the first time R e has been estimated from wastewater. This method provides a low-cost, rapid, and independent way to inform SARS-CoV-2 monitoring during the ongoing pandemic and is applicable to future wastewater-based epidemiology targeting other pathogens. https://doi.org/10.1289/EHP10050.

Generation time of the alpha and delta SARS-CoV-2 variants: an epidemiological analysis

Background

In May, 2021, the delta (B.1.617.2) SARS-CoV-2 variant became dominant in the UK, superseded by the omicron (B.1.1.529) variant in December, 2021. The delta variant is associated with increased transmissibility compared with the alpha variant, which was the dominant variant in the UK between December, 2020, and May, 2021. To understand transmission and the effectiveness of interventions, we aimed to investigate whether the delta variant generation time (the interval between infections in infector–infectee pairs) is shorter—ie, transmissions are happening more quickly—than that of the alpha variant.

Methods

In this epidemiological analysis, we analysed transmission data from an ongoing UK Health Security Agency (UKHSA) prospective household study. Households were recruited to the study after an index case had a positive PCR test and genomic sequencing was used to determine the variant responsible. By fitting a mathematical transmission model to the data, we estimated the intrinsic generation time (which assumes a constant supply of susceptible individuals throughout infection) and the household generation time (which reflects realised transmission in the study households, accounting for susceptible depletion) for the alpha and delta variants.

Findings

Between February and August, 2021, 227 households consisting of 559 participants were recruited to the UKHSA study. The alpha variant was detected or assumed to be responsible for infections in 131 households (243 infections in 334 participants) recruited in February–May, and the delta variant in 96 households (174 infections in 225 participants) in May–August. The mean intrinsic generation time was shorter for the delta variant (4·7 days, 95% credible interval [CI] 4·1–5·6) than the alpha variant (5·5 days, 4·7–6·5), with 92% posterior probability. The mean household generation time was 28% (95% CI 0–48%) shorter for the delta variant (3·2 days, 95% CI 2·5–4·2) than the alpha variant (4·5 days, 3·7–5·4), with 97·5% posterior probability.

Interpretation

The delta variant transmits more quickly in households than the alpha variant, which can be attributed to faster depletion of susceptible individuals in households and a possible decrease in the intrinsic generation time. Interventions such as contact tracing, testing, and isolation might be less effective if transmission of the virus occurs quickly.

Funding

National Institute for Health Research, UK Health Security Agency, Engineering and Physical Sciences Research Council, and UK Research and Innovation.

Epidemiological and genomic findings of the first documented Italian outbreak of SARS-CoV-2 Alpha variant

From 24 December 2020 to 8 February 2021, 163 cases of SARS-CoV-2 Alpha variant of concern (VOC) were identified in Chieti province, Abruzzo region. Epidemiological data allowed the identification of 14 epi-clusters. With one exception, all the epi-clusters were linked to the town of Guardiagrele: 149 contacts formed the network, two-thirds of which were referred to the family/friends context. Real data were then used to estimate transmission parameters. According to our method, the calculated Re(t) was higher than 2 before the 12 December 2020. Similar values were obtained from other studies considering Alpha VOC. Italian sequence data were combined with a random subset of sequences obtained from the GISAID database. Genomic analysis showed close identity between the sequences from Guardiagrele, forming one distinct clade. This would suggest one or limited unspecified viral introductions from outside to Abruzzo region in early December 2020, which led to the diffusion of Alpha VOC in Guardiagrele and in neighbouring municipalities, with very limited inter-regional mixing.

•

SARS-CoV-2 Alpha VOC has been identified in Guardiagrele (Abruzzo, Italy) starting from late December 2020.

•

Epidemiological investigations led to the identification of epi-clusters comprising 163 Alpha VOC cases.

•

A reconstructed transmission chain can be used to estimate transmission parameters including Re(t).

•

A comparison between sequences in the GISAID database supports limited virus introduction scenario in the area.

Wastewater-Based Estimation of the Effective Reproductive Number of SARS-CoV-2

BACKGROUND

The effective reproductive number, Re, is a critical indicator to monitor disease dynamics, inform regional and national policies, and estimate the effectiveness of interventions. It describes the average number of new infections caused by a single infectious person through time. To date, Re estimates are based on clinical data such as observed cases, hospitalizations, and/or deaths. These estimates are temporarily biased when clinical testing or reporting strategies change.

OBJECTIVES

We show that the dynamics of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) RNA in wastewater can be used to estimate Re in near real time, independent of clinical data and without the associated biases.

METHODS

We collected longitudinal measurements of SARS-CoV-2 RNA in wastewater in Zurich, Switzerland, and San Jose, California, USA. We combined this data with information on the temporal dynamics of shedding (the shedding load distribution) to estimate a time series proportional to the daily COVID-19 infection incidence. We estimated a wastewater-based Re from this incidence.

RESULTS

The method to estimate Re from wastewater worked robustly on data from two different countries and two wastewater matrices. The resulting estimates were as similar to the Re estimates from case report data as Re estimates based on observed cases, hospitalizations, and deaths are among each other. We further provide details on the effect of sampling frequency and the shedding load distribution on the ability to infer Re.

DISCUSSION

To our knowledge, this is the first time Re has been estimated from wastewater. This method provides a low-cost, rapid, and independent way to inform SARS-CoV-2 monitoring during the ongoing pandemic and is applicable to future wastewater-based epidemiology targeting other pathogens. https://doi.org/10.1289/EHP10050.

A tentative tracking of the SARS-Cov2 pandemic in France, based on a corrected SIR model including vaccination effects

We developed successive extensions of the SIR model in order to track the dynamics of the SARS-Cov2 disease. The analysis of health system available data is published in a chronicle accessible on the net: https://corona-circule.github.io/lettres/. This chronicle was initiated on late march 2020 and up to now contains 50 issues. A constant concern was the reliability of the data: for instance, we very soon evidenced that the number of confirmed cases, because of the asymptomatic carriers and the erratic testing policy, was hugely underestimated. By the end of 2020 we made a basic change in the model which consisted in accounting for a constant contagiousness time (SIR-tcc) instead of the probabilistic evolution of the end of the infection assumed so far. Recently we completed this SIR-tcc model for the vaccination effects in order to properly track the evolution of the group immunity threshold. Calculations were performed using the Excel facility (Microsoft), allowing a manual fitting of the model parameters. The results have dealt with a large number of countries, but we focus here on the data regarding France. Further pieces of information are also presented, in order to help elucidating some the factors responsible for the complex history of the pandemic dynamics. (submitted dec 14th 2021)

Analysis of COVID-19 Spread in Tokyo through an Agent-Based Model with Data Assimilation

In this paper, we introduce an agent-based model together with a particle filter approach to study the spread of COVID-19. Investigations are mainly performed on the metropolis of Tokyo, but other prefectures of Japan are also briefly surveyed. A novel method for evaluating the effective reproduction number is one of the main outcomes of our approach. Other unknown parameters are also evaluated. Uncertain quantities, such as, for example, the probability that an infected agent develops symptoms, are tested and discussed, and the stability of our computations is examined. Detailed explanations are provided for the model and for the assimilation process.

SARS-CoV-2 transmission potential and rural-urban disease burden disparities across Alabama, Louisiana, and Mississippi, March 2020 - May 2021

PURPOSE

To quantify and compare SARS-CoV-2 transmission potential across Alabama, Louisiana, and Mississippi and selected counties.

METHODS

To determine the time-varying reproduction number R_t of SARS-CoV-2, we applied the R package EpiEstim to the time series of daily incidence of confirmed cases (mid-March 2020 - May 17, 2021) shifted backward by 9 days. Median R_t percentage change when policies changed was determined. Linear regression was performed between log₁₀-transformed cumulative incidence and log₁₀-transformed population size at four time points.

RESULTS

Stay-at-home orders, face mask mandates, and vaccinations were associated with the most significant reductions in SARS-CoV-2 transmission in the three southern states. R_t across the three states decreased significantly by ≥20% following stay-at-home orders. We observed varying degrees of reductions in R_t across states following other policies. Rural Alabama counties experienced higher per capita cumulative cases relative to urban ones as of June 17 and October 17, 2020. Meanwhile, Louisiana and Mississippi saw the disproportionate impact of SARS-CoV-2 in rural counties compared to urban ones throughout the study period.

CONCLUSION

State and county policies had an impact on local pandemic trajectories. The rural-urban disparities in case burden call for evidence-based approaches in tailoring health promotion interventions and vaccination campaigns to rural residents.

Fundamental limits on inferring epidemic resurgence in real time using effective reproduction numbers

We find that epidemic resurgence, defined as an upswing in the effective reproduction number (R) of the contagion from subcritical to supercritical values, is fundamentally difficult to detect in real time. Inherent latencies in pathogen transmission, coupled with smaller and intrinsically noisier case incidence across periods of subcritical spread, mean that resurgence cannot be reliably detected without significant delays of the order of the generation time of the disease, even when case reporting is perfect. In contrast, epidemic suppression (where R falls from supercritical to subcritical values) may be ascertained 5-10 times faster due to the naturally larger incidence at which control actions are generally applied. We prove that these innate limits on detecting resurgence only worsen when spatial or demographic heterogeneities are incorporated. Consequently, we argue that resurgence is more effectively handled proactively, potentially at the expense of false alarms. Timely responses to recrudescent infections or emerging variants of concern are more likely to be possible when policy is informed by a greater quality and diversity of surveillance data than by further optimisation of the statistical models used to process routine outbreak data.

Modeling COVID-19 Incidence by the Renewal Equation after Removal of Administrative Bias and Noise

Simple Summary

In the past two years, the COVID-19 incidence curves and reproduction number Rt have been the main metrics used by policy makers and journalists to monitor the spread of this global pandemic. However, these metrics are not always reliable in the short term, because of a combination of delay in detection, administrative delays and random noise. In this article, we present a complete model of COVID-19 incidence, faithfully reconstructing the incidence curve and reproduction number from the renewal equation of the disease and precisely estimating the biases associated with periodic weekly bias, festive day bias and residual noise.

Abstract

The sanitary crisis of the past two years has focused the public’s attention on quantitative indicators of the spread of the COVID-19 pandemic. The daily reproduction number Rt, defined by the average number of new infections caused by a single infected individual at time t, is one of the best metrics for estimating the epidemic trend. In this paper, we provide a complete observation model for sampled epidemiological incidence signals obtained through periodic administrative measurements. The model is governed by the classic renewal equation using an empirical reproduction kernel, and subject to two perturbations: a time-varying gain with a weekly period and a white observation noise. We estimate this noise model and its parameters by extending a variational inversion of the model recovering its main driving variable Rt. Using Rt, a restored incidence curve, corrected of the weekly and festive day bias, can be deduced through the renewal equation. We verify experimentally on many countries that, once the weekly and festive days bias have been corrected, the difference between the incidence curve and its expected value is well approximated by an exponential distributed white noise multiplied by a power of the magnitude of the restored incidence curve.

Evolution of Responses to COVID-19 and Epidemiological Characteristics in South Korea

The characteristics of COVID-19 have evolved at an accelerated rate over the last two years since the first SARS-CoV-2 case was discovered in December 2019. This evolution is due to the complex interplay among virus, humans, vaccines, and environments, which makes the elucidation of the clinical and epidemiological characteristics of COVID-19 essential to assess ongoing policy responses. In this study, we carry out an extensive retrospective analysis on infection clusters of COVID-19 in South Korea from January 2020 to September 2021 and uncover important clinical and social factors associated with age and regional patterns through the sophisticated large-scale epidemiological investigation using the data provided by the Korea Disease Control and Prevention Agency (KDCA). Epidemiological data of COVID-19 include daily confirmed cases, gender, age, city of residence, date of symptom onset, date of diagnosis, and route of infection. We divide the time span into six major periods based on the characteristics of COVID-19 according to various events such as the rise of new variants, vaccine rollout, change of social distancing levels, and other intervention measures. We explore key features of COVID-19 such as the relationship among unlinked, asymptomatic, and confirmed cases, serial intervals, infector–infectee interactions, and age/region-specific variations. Our results highlight the significant impact of temporal evolution of interventions implemented in South Korea on the characteristics of COVID-19 transmission, in particular, that of a high level of vaccination coverage in the senior-aged group on the dramatic reduction of confirmed cases.

Effectiveness of Localized Lockdowns in the COVID-19 Pandemic

Nonpharmaceutical interventions, such as social distancing and lockdowns, have been essential to control of the coronavirus disease 2019 (COVID-19) pandemic. In particular, localized lockdowns in small geographic areas have become an important policy intervention for preventing viral spread in cases of resurgence. These localized lockdowns can result in lower social and economic costs compared with larger-scale suppression strategies. Using an integrated data set from Chile (March 3-June 15, 2020) and a novel synthetic control approach, we estimated the effect of localized lockdowns, disentangling its direct and indirect causal effects on transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Our results showed that the effects of localized lockdowns are strongly modulated by their duration and are influenced by indirect effects from neighboring geographic areas. Our estimates suggest that extending localized lockdowns can slow down SARS-CoV-2 transmission; however, localized lockdowns on their own are insufficient to control pandemic growth in the presence of indirect effects from contiguous neighboring areas that do not have lockdowns. These results provide critical empirical evidence about the effectiveness of localized lockdowns in interconnected geographic areas.

Epidemicity of cholera spread and the fate of infection control measures

The fate of ongoing infectious disease outbreaks is predicted through reproduction numbers, defining the long-term establishment of the infection, and epidemicity indices, tackling the reactivity of the infectious pool to new contagions. Prognostic metrics of unfolding outbreaks are of particular importance when designing adaptive emergency interventions facing real-time assimilation of epidemiological evidence. Our aim here is twofold. First, we propose a novel form of the epidemicity index for the characterization of cholera epidemics in spatial models of disease spread. Second, we examine in hindsight the survey of infections, treatments and containment measures carried out for the now extinct 2010–2019 Haiti cholera outbreak, to suggest that magnitude and timing of non-pharmaceutical and vaccination interventions imply epidemiological responses recapped by the evolution of epidemicity indices. Achieving negative epidemicity greatly accelerates fading of infections and thus proves a worthwhile target of containment measures. We also show that, in our model, effective reproduction numbers and epidemicity indices are explicitly related. Therefore, providing an upper bound to the effective reproduction number (significantly lower than the unit threshold) warrants negative epidemicity and, in turn, a rapidly fading outbreak preventing coalescence of sparse local sub-threshold flare-ups.

Estimation of Serial Interval and Reproduction Number to Quantify the Transmissibility of SARS-CoV-2 Omicron Variant in South Korea

The omicron variant (B.1.1.529) of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) was the predominant variant in South Korea from late January 2022. In this study, we aimed to report the early estimates of the serial interval distribution and reproduction number to quantify the transmissibility of the omicron variant in South Korea between 25 November 2021 and 31 December 2021. We analyzed 427 local omicron cases and reconstructed 73 transmission pairs. We used a maximum likelihood estimation to assess serial interval distribution from transmission pair data and reproduction numbers from 74 local cases in the first local outbreak. We estimated that the mean serial interval was 3.78 (standard deviation, 0.76) days, which was significantly shorter in child infectors (3.0 days) compared to adult infectors (5.0 days) (p < 0.01). We estimated the mean reproduction number was 1.72 (95% CrI, 1.60−1.85) for the omicron variant during the first local outbreak. Strict adherence to public health measures, particularly in children, should be in place to reduce the transmission risk of the highly transmissible omicron variant in the community.

Incorporating temporal distribution of population-level viral load enables real-time estimation of COVID-19 transmission

Many locations around the world have used real-time estimates of the time-varying effective reproductive number (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}_{t}$$\end{document}Rt) of COVID-19 to provide evidence of transmission intensity to inform control strategies. Estimates of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}_{t}$$\end{document}Rt are typically based on statistical models applied to case counts and typically suffer lags of more than a week because of the latent period and reporting delays. Noting that viral loads tend to decline over time since illness onset, analysis of the distribution of viral loads among confirmed cases can provide insights into epidemic trajectory. Here, we analyzed viral load data on confirmed cases during two local epidemics in Hong Kong, identifying a strong correlation between temporal changes in the distribution of viral loads (measured by RT-qPCR cycle threshold values) and estimates of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}_{t}$$\end{document}Rt based on case counts. We demonstrate that cycle threshold values could be used to improve real-time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}_{t}$$\end{document}Rt estimation, enabling more timely tracking of epidemic dynamics.

The time-varying effective reproductive number (Rt) is useful for monitoring transmission of infections such as COVID-19, but reporting delays impact case count-based estimation methods. Here, the authors demonstrate and validate a method for estimation of Rt based on viral load data from Hong Kong that does not require accurate daily counts.

An investigation of spatial-temporal patterns and predictions of the coronavirus 2019 pandemic in Colombia, 2020-2021

Colombia announced the first case of severe acute respiratory syndrome coronavirus 2 on March 6, 2020. Since then, the country has reported a total of 5,002,387 cases and 127,258 deaths as of October 31, 2021. The aggressive transmission dynamics of SARS-CoV-2 motivate an investigation of COVID-19 at the national and regional levels in Colombia. We utilize the case incidence and mortality data to estimate the transmission potential and generate short-term forecasts of the COVID-19 pandemic to inform the public health policies using previously validated mathematical models. The analysis is augmented by the examination of geographic heterogeneity of COVID-19 at the departmental level along with the investigation of mobility and social media trends. Overall, the national and regional reproduction numbers show sustained disease transmission during the early phase of the pandemic, exhibiting sub-exponential growth dynamics. Whereas the most recent estimates of reproduction number indicate disease containment, with Rt<1.0 as of October 31, 2021. On the forecasting front, the sub-epidemic model performs best at capturing the 30-day ahead COVID-19 trajectory compared to the Richards and generalized logistic growth model. Nevertheless, the spatial variability in the incidence rate patterns across different departments can be grouped into four distinct clusters. As the case incidence surged in July 2020, an increase in mobility patterns was also observed. On the contrary, a spike in the number of tweets indicating the stay-at-home orders was observed in November 2020 when the case incidence had already plateaued, indicating the pandemic fatigue in the country.

Near real-time surveillance of the SARS-CoV-2 epidemic with incomplete data

When responding to infectious disease outbreaks, rapid and accurate estimation of the epidemic trajectory is critical. However, two common data collection problems affect the reliability of the epidemiological data in real time: missing information on the time of first symptoms, and retrospective revision of historical information, including right censoring. Here, we propose an approach to construct epidemic curves in near real time that addresses these two challenges by 1) imputation of dates of symptom onset for reported cases using a dynamically-estimated "backward" reporting delay conditional distribution, and 2) adjustment for right censoring using the NobBS software package to nowcast cases by date of symptom onset. This process allows us to obtain an approximation of the time-varying reproduction number (Rt) in real time. We apply this approach to characterize the early SARS-CoV-2 outbreak in two Spanish regions between March and April 2020. We evaluate how these real-time estimates compare with more complete epidemiological data that became available later. We explore the impact of the different assumptions on the estimates, and compare our estimates with those obtained from commonly used surveillance approaches. Our framework can help improve accuracy, quantify uncertainty, and evaluate frequently unstated assumptions when recovering the epidemic curves from limited data obtained from public health systems in other locations.

Inferring the reproduction number using the renewal equation in heterogeneous epidemics

Real-time estimation of the reproduction number has become the focus of modelling groups around the world as the SARS-CoV-2 pandemic unfolds. One of the most widely adopted means of inference of the reproduction number is via the renewal equation, which uses the incidence of infection and the generation time distribution. In this paper, we derive a multi-type equivalent to the renewal equation to estimate a reproduction number which accounts for heterogeneity in transmissibility including through asymptomatic transmission, symptomatic isolation and vaccination. We demonstrate how use of the renewal equation that misses these heterogeneities can result in biased estimates of the reproduction number. While the bias is small with symptomatic isolation, it can be much larger with asymptomatic transmission or transmission from vaccinated individuals if these groups exhibit substantially different generation time distributions to unvaccinated symptomatic transmitters, whose generation time distribution is often well defined. The bias in estimate becomes larger with greater population size or transmissibility of the poorly characterized group. We apply our methodology to Ebola in West Africa in 2014 and the SARS-CoV-2 in the UK in 2020-2021.

Refining reproduction number estimates to account for unobserved generations of infection in emerging epidemics

Background

Estimating the transmissibility of infectious diseases is key to inform situational awareness and for response planning. Several methods tend to overestimate the basic (R₀) and effective (R_t) reproduction numbers during the initial phases of an epidemic. In this work we explore the impact of incomplete observations and underreporting of the first generations of infections during the initial epidemic phase.

Methods

We propose a debiasing procedure that utilizes a linear exponential growth model to infer unobserved initial generations of infections and apply it to EpiEstim. We assess the performance of our adjustment using simulated data, considering different levels of transmissibility and reporting rates. We also apply the proposed correction to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) incidence data reported in Italy, Sweden, the United Kingdom, and the United States.

Results

In all simulation scenarios, our adjustment outperforms the original EpiEstim method. The proposed correction reduces the systematic bias, and the quantification of uncertainty is more precise, as better coverage of the true R₀ values is achieved with tighter credible intervals. When applied to real-world data, the proposed adjustment produces basic reproduction number estimates that closely match the estimates obtained in other studies while making use of a minimal amount of data.

Conclusions

The proposed adjustment refines the reproduction number estimates obtained with the current EpiEstim implementation by producing improved, more precise estimates earlier than with the original method. This has relevant public health implications.

A semi-parametric, state-space compartmental model with time-dependent parameters for forecasting COVID-19 cases, hospitalizations and deaths

Short-term forecasts of the dynamics of coronavirus disease 2019 (COVID-19) in the period up to its decline following mass vaccination was a task that received much attention but proved difficult to do with high accuracy. However, the availability of standardized forecasts and versioned datasets from this period allows for continued work in this area. Here, we introduce the Gaussian infection state space with time dependence (GISST) forecasting model. We evaluate its performance in one to four weeks ahead forecasts of COVID-19 cases, hospital admissions and deaths in the state of California made with official reports of COVID-19, Google’s mobility reports and vaccination data available each week. Evaluation of these forecasts with a weighted interval score shows them to consistently outperform a naive baseline forecast and often score closer to or better than a high-performing ensemble forecaster. The GISST model also provides parameter estimates for a compartmental model of COVID-19 dynamics, includes a regression submodel for the transmission rate and allows for parameters to vary over time according to a random walk. GISST provides a novel, balanced combination of computational efficiency, model interpretability and applicability to large multivariate datasets that may prove useful in improving the accuracy of infectious disease forecasts.

In-Depth Correlation Analysis of SARS-CoV-2 Effective Reproduction Number and Mobility Patterns: Three Groups of Countries

Objectives

Many governments have imposed—and are still imposing—mobility restrictions to contain the coronavirus disease 2019 (COVID-19) pandemic. However, there is no consensus on whether policy-induced reductions of human mobility effectively reduce the effective reproduction number (Rt) of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Several studies based on country-restricted data reported conflicting trends in the change of the SARS-CoV-2 Rt following mobility restrictions. The objective of this study was to examine, at the global scale, the existence of regional specificities in the correlations between Rt and human mobility.

Methods

We computed the Rt of SARS-CoV-2 using data on worldwide infection cases reported by the Johns Hopkins University, and analyzed the correlation between Rt and mobility indicators from the Google COVID-19 Community Mobility Reports in 125 countries, as well as states/regions within the United States, using the Pearson correlation test, linear modeling, and quadratic modeling.

Results

The correlation analysis identified countries where Rt negatively correlated with residential mobility, as expected by policymakers, but also countries where Rt positively correlated with residential mobility and countries with more complex correlation patterns. The correlations between Rt and residential mobility were non-linear in many countries, indicating an optimal level above which increasing residential mobility is counterproductive.

Conclusions

Our results indicate that, in order to effectively reduce viral circulation, mobility restriction measures must be tailored by region, considering local cultural determinants and social behaviors. We believe that our results have the potential to guide differential refinement of mobility restriction policies at a country/regional resolution.