A Comparative Analysis of Statistical Methods to Estimate the Reproduction Number in Emerging Epidemics, With Implications for the Current Coronavirus Disease 2019 (COVID-19) Pandemic

Increasing situational awareness through nowcasting of the reproduction number

Background

The time-varying reproduction number R is a critical variable for situational awareness during infectious disease outbreaks; however, delays between infection and reporting of cases hinder its accurate estimation in real-time. A number of nowcasting methods, leveraging available information on data consolidation delays, have been proposed to mitigate this problem.

Methods

In this work, we retrospectively validate the use of a nowcasting algorithm during 18 months of the COVID-19 pandemic in Italy by quantitatively assessing its performance against standard methods for the estimation of R.

Results

Nowcasting significantly reduced the median lag in the estimation of R from 13 to 8 days, while concurrently enhancing accuracy. Furthermore, it allowed the detection of periods of epidemic growth with a lead of between 6 and 23 days.

Conclusions

Nowcasting augments epidemic awareness, empowering better informed public health responses.

Nearly Instantaneous Time-Varying Reproduction Number for Contagious Diseases-a Direct Approach Based on Nonlinear Regression

While the world recovers from the COVID-19 pandemic, another outbreak of contagious disease remains the most likely future risk to public safety. Now is therefore the time to equip health authorities with effective tools to ensure they are operationally prepared for future events. We propose a direct approach to obtain reliable nearly instantaneous time-varying reproduction numbers for contagious diseases, using only the number of infected individuals as input and utilising the dynamics of the susceptible-infected-recovered (SIR) model. Our approach is based on a multivariate nonlinear regression model simultaneously assessing parameters describing the transmission and recovery rate as a function of the SIR model. Shortly after start of a pandemic, our approach enables estimation of daily reproduction numbers. It avoids numerous sources of additional variation and provides a generic tool for monitoring the instantaneous reproduction numbers. We use Norwegian COVID-19 data as case study and demonstrate that our results are well aligned with changes in the number of infected individuals and the change points following policy interventions. Our estimated reproduction numbers are notably less volatile, provide more credible short-time predictions for the number of infected individuals, and are thus clearly favorable compared with the results obtained by two other popular approaches used for monitoring a pandemic. The proposed approach contributes to increased preparedness to future pandemics of contagious diseases, as it can be used as a simple yet powerful tool to monitor the pandemics, provide short-term predictions, and thus support decision making regarding timely and targeted control measures.

Why are different estimates of the effective reproductive number so different? A case study on COVID-19 in Germany

The effective reproductive number Rt has taken a central role in the scientific, political, and public discussion during the COVID-19 pandemic, with numerous real-time estimates of this quantity routinely published. Disagreement between estimates can be substantial and may lead to confusion among decision-makers and the general public. In this work, we compare different estimates of the national-level effective reproductive number of COVID-19 in Germany in 2020 and 2021. We consider the agreement between estimates from the same method but published at different time points (within-method agreement) as well as retrospective agreement across eight different approaches (between-method agreement). Concerning the former, estimates from some methods are very stable over time and hardly subject to revisions, while others display considerable fluctuations. To evaluate between-method agreement, we reproduce the estimates generated by different groups using a variety of statistical approaches, standardizing analytical choices to assess how they contribute to the observed disagreement. These analytical choices include the data source, data pre-processing, assumed generation time distribution, statistical tuning parameters, and various delay distributions. We find that in practice, these auxiliary choices in the estimation of Rt may affect results at least as strongly as the selection of the statistical approach. They should thus be communicated transparently along with the estimates.

Assessing the heterogeneity in the transmission of infectious diseases from time series of epidemiological data

Structural features and the heterogeneity of disease transmissions play an essential role in the dynamics of epidemic spread. But these aspects can not completely be assessed from aggregate data or macroscopic indicators such as the effective reproduction number. We propose in this paper an index of effective aggregate dispersion (EffDI) that indicates the significance of infection clusters and superspreading events in the progression of outbreaks by carefully measuring the level of relative stochasticity in time series of reported case numbers using a specially crafted statistical model for reproduction. This allows to detect potential transitions from predominantly clustered spreading to a diffusive regime with diminishing significance of singular clusters, which can be a decisive turning point in the progression of outbreaks and relevant in the planning of containment measures. We evaluate EffDI for SARS-CoV-2 case data in different countries and compare the results with a quantifier for the socio-demographic heterogeneity in disease transmissions in a case study to substantiate that EffDI qualifies as a measure for the heterogeneity in transmission dynamics.

Brain Disorders: Impact of Mild SARS-CoV-2 May Shrink Several Parts of the Brain

Coronavirus (COVID-19) is a highly infectious respiratory infection discovered in Wuhan, China, in December 2019. As a result of the pandemic, several individuals have experienced life-threatening diseases, the loss of loved ones, lockdowns, isolation, an increase in unemployment, and household conflict. Moreover, COVID-19 may cause direct brain injury via encephalopathy. The long-term impacts of this virus on mental health and brain function need to be analysed by researchers in the coming years. This article aims to describe the prolonged neurological clinical consequences related to brain changes in people with mild COVID-19 infection. When compared to a control group, people those who tested positive for COVID-19 had more brain shrinkage, grey matter shrinkage, and tissue damage. The damage occurs predominantly in areas of the brain that are associated with odour, ambiguity, strokes, reduced attention, headaches, sensory abnormalities, depression, and mental abilities for few months after the first infection. Therefore, in patients after a severe clinical condition of COVID-19, a deepening of persistent neurological signs is necessary.

A comparative study on the three calculation methods for reproduction numbers of COVID-19

Objective

This study uses four COVID-19 outbreaks as examples to calculate and compare merits and demerits, as well as applicational scenarios, of three methods for calculating reproduction numbers.

Method

The epidemiological characteristics of the COVID-19 outbreaks are described. Through the definition method, the next-generation matrix-based method, and the epidemic curve and serial interval (SI)-based method, corresponding reproduction numbers were obtained and compared.

Results

Reproduction numbers (R eff ), obtained by the definition method of the four regions, are 1.20, 1.14, 1.66, and 1.12. Through the next generation matrix method, in region H R eff = 4.30, 0.44; region P R eff = 6.5, 1.39, 0; region X R eff = 6.82, 1.39, 0; and region Z R eff = 2.99, 0.65. Time-varying reproduction numbers (R t ), which are attained by SI of onset dates, are decreasing with time. Region H reached its highest R t = 2.8 on July 29 and decreased to R t < 1 after August 4; region P reached its highest R t = 5.8 on September 9 and dropped to R t < 1 by September 14; region X had a fluctuation in the R t and R t < 1 after September 22; R t in region Z reached a maximum of 1.8 on September 15 and decreased continuously to R t < 1 on September 19.

Conclusion

The reproduction number obtained by the definition method is optimal in the early stage of epidemics with a small number of cases that have clear transmission chains to predict the trend of epidemics accurately. The effective reproduction number R eff , calculated by the next generation matrix, could assess the scale of the epidemic and be used to evaluate the effectiveness of prevention and control measures used in epidemics with a large number of cases. Time-varying reproduction number R t , obtained via epidemic curve and SI, can give a clear picture of the change in transmissibility over time, but the conditions of use are more rigorous, requiring a greater sample size and clear transmission chains to perform the calculation. The rational use of the three methods for reproduction numbers plays a role in the further study of the transmissibility of COVID-19.

The role of inter-regional mobility in forecasting SARS-CoV-2 transmission

In this paper, we present a method to forecast the spread of SARS-CoV-2 across regions with a focus on the role of mobility. Mobility has previously been shown to play a significant role in the spread of the virus, particularly between regions. Here, we investigate under which epidemiological circumstances incorporating mobility into transmission models yields improvements in the accuracy of forecasting, where we take the situation in The Netherlands during and after the first wave of transmission in 2020 as a case study. We assess the quality of forecasting on the detailed level of municipalities, instead of on a nationwide level. To model transmissions, we use a simple mobility-enhanced SEIR compartmental model with subpopulations corresponding to the Dutch municipalities. We use commuter information to quantify mobility, and develop a method based on maximum likelihood estimation to determine the other relevant parameters. We show that taking inter-regional mobility into account generally leads to an improvement in forecast quality. However, at times when policies are in place that aim to reduce contacts or travel, this improvement is very small. By contrast, the improvement becomes larger when municipalities have a relatively large amount of incoming mobility compared with the number of inhabitants.

Estimating the basic reproduction number from noisy daily data

In this paper, we propose an easy to implement generalized linear models (GLM) methodology for estimating the basic reproduction number, R₀, a major epidemic parameter for assessing the transmissibility of an infection. Our approach rests on well known qualitative properties of the classical SIR and SEIR systems for large populations. Moreover, we assume that information at the individual network level is not available. In inference we consider non homogeneous Poisson observation processes and mainly concentrate on epidemics that spread through a completely susceptible population. Further, we examine the performance of the estimator under various scenarios of relevance in practice, like partially observed data. We perform a detailed simulation study and illustrate our approach on Covid-19 Canadian data sets. Finally, we present extensions of our methodology and discuss its merits and practical limitations, in particular the challenges in estimating R₀ when mitigation measures are applied.

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.

Trade, uneven development and people in motion: Used territories and the initial spread of COVID-19 in Mesoamerica and the Caribbean

Mesoamerica and the Caribbean form a region comprised by middle- and low-income countries affected by the COVID-19 pandemic differently. Here, we ask whether the spread of COVID-19, measured using early epidemic growth rates (r), reproduction numbers (R _t ), accumulated cases, and deaths, is influenced by how the 'used territories' across the regions have been differently shaped by uneven development, human movement and trade differences. Using an econometric approach, we found that trade openness increased cases and deaths, while the number of international cities connected at main airports increased r, cases and deaths. Similarly, increases in concentration of imports, a sign of uneven development, coincided with increases in early epidemic growth and deaths. These results suggest that countries whose used territory was defined by a less uneven development were less likely to show exacerbated COVID-19 patterns of transmission. Health outcomes were worst in more trade-dependent countries, even after controlling for the impact of transmission prevention and mitigation policies, highlighting how structural effects of economic integration in used territories were associated with the initial COVID-19 spread in Mesoamerica and the Caribbean.

Impact of tiered restrictions on human activities and the epidemiology of the second wave of COVID-19 in Italy

To counter the second COVID-19 wave in autumn 2020, the Italian government introduced a system of physical distancing measures organized in progressively restrictive tiers (coded as yellow, orange, and red) imposed on a regional basis according to real-time epidemiological risk assessments. We leverage the data from the Italian COVID-19 integrated surveillance system and publicly available mobility data to evaluate the impact of the three-tiered regional restriction system on human activities, SARS-CoV-2 transmissibility and hospitalization burden in Italy. The individuals’ attendance to locations outside the residential settings was progressively reduced with tiers, but less than during the national lockdown against the first COVID-19 wave in the spring. The reproduction number R(t) decreased below the epidemic threshold in 85 out of 107 provinces after the introduction of the tier system, reaching average values of about 0.95-1.02 in the yellow tier, 0.80-0.93 in the orange tier and 0.74-0.83 in the red tier. We estimate that the reduced transmissibility resulted in averting about 36% of the hospitalizations between November 6 and November 25, 2020. These results are instrumental to inform public health efforts aimed at preventing future resurgence of cases.

Italy introduced a system of tiered SARS-CoV-2 control measures in November 2020. Here, the authors quantify the effect of these measures on SARS-CoV-2 transmissibility and hospitalisation, and find reductions across all tiers with the greatest impacts associated with the most restrictive level.

A mechanistic and data-driven reconstruction of the time-varying reproduction number: Application to the COVID-19 epidemic

The effective reproduction number Reff is a critical epidemiological parameter that characterizes the transmissibility of a pathogen. However, this parameter is difficult to estimate in the presence of silent transmission and/or significant temporal variation in case reporting. This variation can occur due to the lack of timely or appropriate testing, public health interventions and/or changes in human behavior during an epidemic. This is exactly the situation we are confronted with during this COVID-19 pandemic. In this work, we propose to estimate Reff for the SARS-CoV-2 (the etiological agent of the COVID-19), based on a model of its propagation considering a time-varying transmission rate. This rate is modeled by a Brownian diffusion process embedded in a stochastic model. The model is then fitted by Bayesian inference (particle Markov Chain Monte Carlo method) using multiple well-documented hospital datasets from several regions in France and in Ireland. This mechanistic modeling framework enables us to reconstruct the temporal evolution of the transmission rate of the COVID-19 based only on the available data. Except for the specific model structure, it is non-specifically assumed that the transmission rate follows a basic stochastic process constrained by the observations. This approach allows us to follow both the course of the COVID-19 epidemic and the temporal evolution of its Reff(t). Besides, it allows to assess and to interpret the evolution of transmission with respect to the mitigation strategies implemented to control the epidemic waves in France and in Ireland. We can thus estimate a reduction of more than 80% for the first wave in all the studied regions but a smaller reduction for the second wave when the epidemic was less active, around 45% in France but just 20% in Ireland. For the third wave in Ireland the reduction was again significant (>70%).

Time-varying Reproduction Numbers of COVID-19 in Georgia, USA, March 2, 2020 to November 20, 2020

BACKGROUND

In 2020, Severe Acute Respiratory Syndrome Coronavirus 2 impacted Georgia, USA. Georgia announced a state-wide shelter-in-place on April 2 and partially lifted restrictions on April 27. We estimated the time-varying reproduction numbers (Rt) of COVID-19 in Georgia, Metro Atlanta, and Dougherty County and environs from March 2, 2020, to November 20, 2020.

METHODS

We analyzed the daily incidence of confirmed COVID-19 cases in Georgia, Metro Atlanta, and Dougherty County and its surrounding counties, and estimated Rt using the R package EpiEstim. We used a 9-day correction for the date of report to analyze the data by assumed date of infection.

RESULTS

The median Rt estimate in Georgia dropped from between 2 and 4 in mid-March to < 2 in late March to around 1 from mid-April to November. Regarding Metro Atlanta, Rt fluctuated above 1.5 in March and around 1 since April. In Dougherty County, the median Rt declined from around 2 in late March to 0.32 on April 26. Then, Rt fluctuated around 1 in May through November. Counties surrounding Dougherty County registered an increase in Rt estimates days after a superspreading event occurred in the area.

CONCLUSIONS

In Spring 2020, Severe Acute Respiratory Syndrome Coronavirus 2 transmission in Georgia declined likely because of social distancing measures. However, because restrictions were relaxed in late April and elections were conducted in November, community transmission continued, with Rt fluctuating around 1 across Georgia, Metro Atlanta, and Dougherty County as of November 2020. The superspreading event in Dougherty County affected surrounding areas, indicating the possibility of local transmission in neighboring counties.

Disease momentum: Estimating the reproduction number in the presence of superspreading

A primary quantity of interest in the study of infectious diseases is the average number of new infections that an infected person produces. This so-called reproduction number has significant implications for the disease progression. There has been increasing literature suggesting that superspreading, the significant variability in number of new infections caused by individuals, plays an important role in the spread of SARS-CoV-2. In this paper, we consider the effect that such superspreading has on the estimation of the reproduction number and subsequent estimates of future cases. Accordingly, we employ a simple extension to models currently used in the literature to estimate the reproduction number and present a case-study of the progression of COVID-19 in Austria. Our models demonstrate that the estimation uncertainty of the reproduction number increases with superspreading and that this improves the performance of prediction intervals. Of independent interest is the derivation of a transparent formula that connects the extent of superspreading to the width of credible intervals for the reproduction number. This serves as a valuable heuristic for understanding the uncertainty surrounding diseases with superspreading.

SARS-CoV-2 Transmission in Alberta, British Columbia, and Ontario, Canada, December 25, 2019, to December 1, 2020

OBJECTIVE

This study aimed to investigate coronavirus disease (COVID-19) epidemiology in Alberta, British Columbia, and Ontario, Canada.

METHODS

Using data through December 1, 2020, we estimated time-varying reproduction number, Rt, using EpiEstim package in R, and calculated incidence rate ratios (IRR) across the 3 provinces.

RESULTS

In Ontario, 76% (92 745/121 745) of cases were in Toronto, Peel, York, Ottawa, and Durham; in Alberta, 82% (49 878/61 169) in Calgary and Edmonton; in British Columbia, 90% (31 142/34 699) in Fraser and Vancouver Coastal. Across 3 provinces, Rt dropped to ≤ 1 after April. In Ontario, Rt would remain < 1 in April if congregate-setting-associated cases were excluded. Over summer, Rt maintained < 1 in Ontario, ~1 in British Columbia, and ~1 in Alberta, except early July when Rt was > 1. In all 3 provinces, Rt was > 1, reflecting surges in case count from September through November. Compared with British Columbia (684.2 cases per 100 000), Alberta (IRR = 2.0; 1399.3 cases per 100 000) and Ontario (IRR = 1.2; 835.8 cases per 100 000) had a higher cumulative case count per 100 000 population.

CONCLUSIONS

Alberta and Ontario had a higher incidence rate than British Columbia, but Rt trajectories were similar across all 3 provinces.

Epidemiology and Clinical Course of First Wave Coronavirus Disease Cases, Faroe Islands

The Faroe Islands was one of the first countries in the Western Hemisphere to eliminate coronavirus disease (COVID-19). During the first epidemic wave in the country, 187 cases were reported between March 3 and April 22, 2020. Large-scale testing and thorough contact tracing were implemented early on, along with lockdown measures. Transmission chains were mapped through patient history and knowledge of contact with prior cases. The most common reported COVID-19 symptoms were fever, headache, and cough, but 11.2% of cases were asymptomatic. Among 187 cases, 8 patients were admitted to hospitals but none were admitted to intensive care units and no deaths occurred. Superspreading was evident during the epidemic because most secondary cases were attributed to just 3 infectors. Even with the high incidence rate in early March, the Faroe Islands successfully eliminated the first wave of COVID-19 through the early use of contact tracing, quarantine, social distancing, and large-scale testing.