Instantaneous Reproduction Number Research Articles

An Efficient Approach to Nowcasting the Time-varying Reproduction Number.

Estimating the instantaneous reproduction number () in near real time is crucial for monitoring and responding to epidemic outbreaks on a daily basis. However, such estimates often suffer from bias due to reporting delays inherent in surveillance systems. We propose a fast and flexible Bayesian methodology to overcome this challenge by estimating while taking into account reporting delays. Furthermore, the method naturally takes into account the uncertainty associated with the nowcasting of cases to get a valid uncertainty estimation of the nowcasted reproduction number. We evaluate the proposed methodology through a simulation study and apply it to COVID-19 incidence data in Belgium.

An Intense Out-of-Season Rebound of Influenza Activity After the Relaxation of Coronavirus Disease 2019 Restrictions in Beijing, China.

The aim of this study was to investigate the changes of epidemic characteristics of influenza activity pre- and post-coronavirus disease 2019 (COVID-19) in Beijing, China. Epidemiologic data were collected from the influenza surveillance system in Beijing. We compared epidemic intensity, epidemic onset and duration, and influenza transmissibility during the 2022-2023 season with pre-COVID-19 seasons from 2014 to 2020. The overall incidence rate of influenza in the 2022-2023 season was significantly higher than that of the pre-COVID-19 period, with the record-high level of epidemic intensity in Beijing. The onset and duration of the influenza epidemic period in 2022-2023 season was notably later and shorter than that of the 2014-2020 seasons. Maximum daily instantaneous reproduction number (Rt) of the 2022-2023 season (Rt = 2.31) was much higher than that of the pre-COVID-19 period (Rt = 1.49). The incidence of influenza A(H1N1) and A(H3N2) were the highest among children aged 0-4 years and 5-14 years, respectively, in the 2022-2023 season. A late, intense, and short-term peak influenza activity was observed in the 2022-2023 season in Beijing. Children <15 years old were impacted the most by the interruption of influenza circulation during the COVID-19 pandemic. Maintaining continuous surveillance and developing targeted public health strategies of influenza is necessary.

Epidemiological findings, estimates of the instantaneous reproduction number, and control strategies of the first Mpox outbreak in Latin America

BackgroundThe 2022–2023 period marked the largest global Mpox outbreak, with Latin America's situation notably underexplored. This study aims to estimate Mpox's instantaneous reproduction number (R(t)), analyze epidemiological trends, and map vaccination efforts in six Latin American countries. MethodsUtilizing Pan American Health Organization Mpox surveillance data, we examined demographic characteristics, cumulative incidence rates, and epidemic curves, calculated R(t) with weekly sliding windows for each country, alongside a review of vaccination initiatives. ResultsFrom 2022 to 2023, 25,503 Mpox cases and 71 deaths were reported across Argentina, Brazil, Chile, Colombia, Mexico and Peru, with a significant majority (91.8%–98.5%) affecting men, with a mean age of 32–35 years. Maximum R(t) values varied across countries: Argentina (2.63; 0.85 to 5.39), Brazil (3.13; 2.61 to 3.69), Chile (2.91; 1.55 to 4.70), Colombia (3.15; 2.07 to 4.44), Mexico (2.28; 1.18 to 3.75), and Peru (2.84; 2.33 to 3.40). The epidemic's peak occurred between August and September 2022 with R(t) values subsequently dropping below 1. From November 2022, and as of February 2024, only Chile, Peru, and Brazil had initiated Mpox vaccination campaigns, with Colombia launching a Clinical Trial. ConclusionThe peak of the Mpox epidemic in the studied countries occurred before the commencement of vaccination programs. This trend may be then partly attributed to a combination of behavioral modifications in key affected communities and contact tracing local programs. Therefore, the proportion of the at-risk population that remains susceptible is still uncertain, highlighting the need for continued surveillance and evaluation of vaccination strategies.

Association between ozone and influenza transmissibility in China

BackgroundCommon air pollutants such as ozone (O3), sulfur dioxide (SO2), nitrogen dioxide (NO2), and particulate matter play significant roles as influential factors in influenza-like illness (ILI). However, evidence regarding the impact of O3 on influenza transmissibility in multi-subtropical regions is limited, and our understanding of the effects of O3 on influenza transmissibility in temperate regions remain unknown.MethodsWe studied the transmissibility of influenza in eight provinces across both temperate and subtropical regions in China based on 2013 to 2018 provincial-level surveillance data on influenza-like illness (ILI) incidence and viral activity. We estimated influenza transmissibility by using the instantaneous reproduction number ({R}_{t}) and examined the relationships between transmissibility and daily O3 concentrations, air temperature, humidity, and school holidays. We developed a multivariable regression model for {R}_{t} to quantify the contribution of O3 to variations in transmissibility.ResultsOur findings revealed a significant association between O3 and influenza transmissibility. In Beijing, Tianjin, Shanghai and Jiangsu, the association exhibited a U-shaped trend. In Liaoning, Gansu, Hunan, and Guangdong, the association was L-shaped. When aggregating data across all eight provinces, a U-shaped association was emerged. O3 was able to accounted for up to 13% of the variance in {R}_{t}. O3 plus other environmental drivers including mean daily temperature, relative humidity, absolute humidity, and school holidays explained up to 20% of the variance in {R}_{t}.ConclusionsO3 was a significant driver of influenza transmissibility, and the association between O3 and influenza transmissibility tended to display a U-shaped pattern.

Using a Bayesian hierarchical approach to study the association between non-pharmaceutical interventions and the spread of Covid-19 in Germany

Non-Pharmaceutical Interventions (NPIs) are community mitigation strategies, aimed at reducing the spread of illnesses like the coronavirus pandemic, without relying on pharmaceutical drug treatments. This study aims to evaluate the effectiveness of different NPIs across sixteen states of Germany, for a time period of 21 months of the pandemic. We used a Bayesian hierarchical approach that combines different sub-models and merges information from complementary sources, to estimate the true and unknown number of infections. In this framework, we used data on reported cases, hospitalizations, intensive care unit occupancy, and deaths to estimate the effect of NPIs. The list of NPIs includes: “contact restriction (up to 5 people)”, “strict contact restriction”, “curfew”, “events permitted up to 100 people”, “mask requirement in shopping malls”, “restaurant closure”, “restaurants permitted only with test”, “school closure” and “general behavioral changes”. We found a considerable reduction in the instantaneous reproduction number by “general behavioral changes”, “strict contact restriction”, “restaurants permitted only with test”, “contact restriction (up to 5 people)”, “restaurant closure” and “curfew”. No association with school closures could be found. This study suggests that some public health measures, including general behavioral changes, strict contact restrictions, and restaurants permitted only with tests are associated with containing the Covid-19 pandemic. Future research is needed to better understand the effectiveness of NPIs in the context of Covid-19 vaccination.

Population mobility change for controlling the transmission of COVID-19: mobile phone data analysis in nine cities of China

ABSTRACT Mobility restriction measures were the main tools to control the spread of COVID-19, but the extent to which the mobility has decreased remained unsure. We investigated the change in local population mobility and its correlation with COVID-19 infections, using 1185 billion aggregated mobile phone data records in nine main cities in China from 10 January to 24 February 2020. The mobility fell by as much as 79.57% compared to the normal days in 2020 and by 58.13% compared to the same lunar period in 2019. The daily incidence of COVID-19 was significantly correlated with local daily mobility (R2 = 0.77, P < 0.001). The instantaneous reproduction number R(t) declined by 3% when mobility was reduced by 10% in the GLM analysis (P < 0.05). Our study indicated that the decreased mobility level, driven by a mixture effect of holiday and public health interventions, could substantially reduce the transmission of COVID-19 to a low level. Our study could provide evidence of mobility restriction to control local transmission for other places facing COVID-19 outbreaks or potential next waves.

Epidemiological and genomic investigation of chikungunya virus in Rio de Janeiro state, Brazil, between 2015 and 2018.

Since 2014, Brazil has experienced an unprecedented epidemic caused by chikungunya virus (CHIKV), with several waves of East-Central-South-African (ECSA) lineage transmission reported across the country. In 2018, Rio de Janeiro state, the third most populous state in Brazil, reported 41% of all chikungunya cases in the country. Here we use evolutionary and epidemiological analysis to estimate the timescale of CHIKV-ECSA-American lineage and its epidemiological patterns in Rio de Janeiro. We show that the CHIKV-ECSA outbreak in Rio de Janeiro derived from two distinct clades introduced from the Northeast region in mid-2015 (clade RJ1, n = 63/67 genomes from Rio de Janeiro) and mid-2017 (clade RJ2, n = 4/67). We detected evidence for positive selection in non-structural proteins linked with viral replication in the RJ1 clade (clade-defining: nsP4-A481D) and the RJ2 clade (nsP1-D531G). Finally, we estimate the CHIKV-ECSA's basic reproduction number (R0) to be between 1.2 to 1.6 and show that its instantaneous reproduction number (Rt) displays a strong seasonal pattern with peaks in transmission coinciding with periods of high Aedes aegypti transmission potential. Our results highlight the need for continued genomic and epidemiological surveillance of CHIKV in Brazil, particularly during periods of high ecological suitability, and show that selective pressures underline the emergence and evolution of the large urban CHIKV-ECSA outbreak in Rio de Janeiro.

Instantaneous reproduction number and epidemic growth rate for predicting COVID-19 waves: the first 2 years of the pandemic in Spain.

Several indicators were employed to manage the COVID-19 pandemic. In this study, our objective was to compare the instantaneous reproductive number and the epidemic growth rate in the Spanish population. Data on daily numbers of cases, admissions into hospitals, admissions into ICUs, and deaths due to COVID-19 in Spain from March 2020 to March 2022 were obtained. The four "pandemic state indicators", which are daily numbers of cases, admissions into hospitals, admissions into ICUs, and deaths due to COVID-19 in Spain from March 2020 to March 2022 were obtained from the Instituto de Salud Carlos III. The epidemic growth rate was estimated as the derivative of the natural logarithm of daily cases with respect to time. Both the reproductive number and the growth rate, as "pandemic trend indicators," were evaluated according to their capacity to anticipate waves as "pandemic state indicators." Using both the reproductive number and the epidemic growth rate, we were able to anticipate most COVID-19 waves. In most waves, the more severe the presentation of COVID-19, the more effective the pandemic trend indicators would be. Besides daily number of cases or other measures of disease frequency, the epidemic growth rate and the reproductive number have different roles in measuring the trend of an epidemic. Naïve interpretations and the use of any indicator as a unique value to make decisions should be discouraged.

Data-driven estimation of the instantaneous reproduction number and growth rates for the 2022 monkeypox outbreak in Europe.

To estimate the instantaneous reproduction number Rt and the epidemic growth rates for the 2022 monkeypox outbreaks in the European region. We gathered daily laboratory-confirmed monkeypox cases in the most affected European countries from the beginning of the outbreak to September 23, 2022. A data-driven estimation of the instantaneous reproduction number is obtained using a novel filtering type Bayesian inference. A phenomenological growth model coupled with a Bayesian sequential approach to update forecasts over time is used to obtain time-dependent growth rates in several countries. The instantaneous reproduction number Rt for the laboratory-confirmed monkeypox cases in Spain, France, Germany, the UK, the Netherlands, Portugal, and Italy. At the early phase of the outbreak, our estimation for Rt, which can be used as a proxy for the basic reproduction number R0, was 2.06 (95% CI 1.63 - 2.54) for Spain, 2.62 (95% CI 2.23 - 3.17) for France, 2.81 (95% CI 2.51 - 3.09) for Germany, 1.82 (95% CI 1.52 - 2.18) for the UK, 2.84 (95% CI 2.07 - 3.91) for the Netherlands, 1.13 (95% CI 0.99 - 1.32) for Portugal, 3.06 (95% CI 2.48 - 3.62) for Italy. Cumulative cases for these countries present subexponential rather than exponential growth dynamics. Our findings suggest that the current monkeypox outbreaks present limited transmission chains of human-to-human secondary infection so the possibility of a huge pandemic is very low. Confirmed monkeypox cases are decreasing significantly in the European region, the decline might be attributed to public health interventions and behavioral changes in the population due to increased risk perception. Nevertheless, further strategies toward elimination are essential to avoid the subsequent evolution of the monkeypox virus that can result in new outbreaks.

Clinical, epidemiological, and genomic characteristics of a seasonal influenza A virus outbreak in Beijing: A descriptive study.

China experienced a severe influenza season that began at the end of February 2023. The aim of this post hoc analysis was to investigate the clinical, epidemiological, and genomic features of this outbreak in Beijing. The number of cases increased rapidly from the end of February and reached its peak in March, with 7262 confirmed cases included in this study. The median age was 33 years, and 50.3% of them were male. The average daily positive rate reached 69% during the peak period. The instantaneous reproduction number (Rt) showed a median of 2.1, exceeded 2.5 initially, and remaining above 1 for the following month. The most common symptoms were fever (75.0%), cough (51.0%), and expectoration (42.9%), with a median body temperature of 38.5°C (interquartile range 38-39). Eight clinical symptoms were more likely to be observed in cases with fever, with odds ratio greater than 1. Viral shedding time ranged from 3 to 25 days, with median of 7.5 days. The circulating viruses in Beijing mainly included H1N1pdm09 (clades 5a.2a and 5a.2a.1), following with H3N2 (clade 2a.2a.3a.1). The descriptive study suggests that influenza viruses in this influenza season had a higher transmissibility and longer shedding duration, with fever being the most common symptom.

Effects of public-health measures for zeroing out different SARS-CoV-2 variants

Targeted public health interventions for an emerging epidemic are essential for preventing pandemics. During 2020-2022, China invested significant efforts in strict zero-COVID measures to contain outbreaks of varying scales caused by different SARS-CoV-2 variants. Based on a multi-year empirical dataset containing 131 outbreaks observed in China from April 2020 to May 2022 and simulated scenarios, we ranked the relative intervention effectiveness by their reduction in instantaneous reproduction number. We found that, overall, social distancing measures (38% reduction, 95% prediction interval 31-45%), face masks (30%, 17-42%) and close contact tracing (28%, 24-31%) were most effective. Contact tracing was crucial in containing outbreaks during the initial phases, while social distancing measures became increasingly prominent as the spread persisted. In addition, infections with higher transmissibility and a shorter latent period posed more challenges for these measures. Our findings provide quantitative evidence on the effects of public-health measures for zeroing out emerging contagions in different contexts.

The association between ambient pollutants and influenza transmissibility: A nationwide study involving 30 provinces in China.

The impact of exposure to ambient pollutants on influenza transmissibility is poorly understood. We aim to examine the associations of six ambient pollutants with influenza transmissibility in China and assess the effect of the depletion of susceptibles. Provincial-level surveillance data on weekly influenza-like illness (ILI) incidence and viral activity were utilized to estimate the instantaneous reproduction number (Rt) using spline functions. Log-linear regression and the distributed lag non-linear model (DLNM) were employed to investigate the effects of ambient pollutants-ozone (O3), particulate matter ≤2.5μm (PM2.5), particulate matter ≤10μm (PM10), nitrogen dioxide (NO2), sulfur dioxide (SO2), and carbon monoxide (CO)-on influenza transmissibility across 30 Chinese provinces from 2014 to 2019. Additionally, the potential effects of the depletion of susceptibles and regional characteristics were explored. There is a significantly positive correlation between influenza transmissibility and five distinct ambient pollutants: PM2.5, PM10, SO2, CO, and NO2. On average, these ambient pollutants explained percentages of the variance in Rt: 0.8%, 0.8%, 1.9%, 1.3%, and 1.4%, respectively. Conversely, O3 was found to be negatively associated with Rt, explaining 1.5% of the variance in Rt. When controlling for the effect of susceptibles depletion, the effects of all pollutants were more pronounced. The effects of PM2.5, PM10, CO, and SO2 were higher in the eastern and southern regions. Most ambient pollutants may potentially contribute to the facilitation of human-to-human influenza virus transmission in China. This observed association was maintained even after adjusting for variation in the susceptible population.

Did national holidays accelerate COVID-19 diffusion during the first phase of the pandemic in Bangladesh?

Bangladesh registered 20,117,32 confirmed cases of COVID-19 and the death toll crossed the grim milestone of 29,323 across the country as of August 31st, 2022. Despite the enforcement of stringent COVID-19 measures, the country witnessed an accelerated diffusion of coronavirus cases during the national events, inclusive of short festivals, in 2020. The present study aims to examine the association between these national holidays and the COVID-19 trasmission rate in Bangladesh. We employed a mathematical model and calculated the instantaneous reproduction number, Rt, of the 64 districts in Bangladesh to check the dynamics of COVID-19 diffusion. The comprehensive analysis shows a notable escalation of Rt value and thus the enhanced transmission rate in Dhaka and in all industrialized cities during the major events such as, garments reopening and religious holidays in Bangladesh. We further showcase the COVID-19 diffusion explicitly in Dhaka Division at the first phase of the pandemic in Bangladesh. Based on our analysis, a set of measures, including restricted public mobility and the celebration of festivals, alongside improving the public’s awareness of the situation, has been recommended to evade the future pandemic risks while running the national festival activities in Bangladesh.

Modeling a traffic light warning system for acute respiratory infections

The high morbidity of acute respiratory infections constitutes a crucial global health burden. In particular, for SARS-CoV-2, non-pharmaceutical intervention geared to enforce social distancing policies, vaccination, and treatments will remain an essential part of public health policies to mitigate and control disease outbreaks. However, the implementation of mitigation measures directed to increase social distancing when the risk of contagion is a complex enterprise because of the impact of NPI on beliefs, political views, economic issues, and, in general, public perception. The way of implementing these mitigation policies studied in this work is the so-called traffic-light monitoring system that attempts to regulate the application of measures that include restrictions on mobility and the size of meetings, among other non-pharmaceutical strategies. Balanced enforcement and relaxation of measures guided through a traffic-light system that considers public risk perception and economic costs may improve the public health benefit of the policies while reducing their cost. We derive a model for the epidemiological traffic-light policies based on the best response for trigger measures driven by the risk perception of people, instantaneous reproduction number, and the prevalence of a hypothetical acute respiratory infection. With numerical experiments, we evaluate and identify the role of appreciation from a hypothetical controller that could opt for protocols aligned with the cost due to the burden of the underlying disease and the economic cost of implementing measures. As the world faces new acute respiratory outbreaks, our results provide a methodology to evaluate and develop traffic light policies resulting from a delicate balance between health benefits and economic implications.

Impact of Human Mobility on COVID-19 Transmission According to Mobility Distance, Location, and Demographic Factors in the Greater Bay Area of China: Population-Based Study.

Mobility restriction was one of the primary measures used to restrain the spread of COVID-19 globally. Governments implemented and relaxed various mobility restriction measures in the absence of evidence for almost 3 years, which caused severe adverse outcomes in terms of health, society, and economy. This study aimed to quantify the impact of mobility reduction on COVID-19 transmission according to mobility distance, location, and demographic factors in order to identify hotspots of transmission and guide public health policies. Large volumes of anonymized aggregated mobile phone position data between January 1 and February 24, 2020, were collected for 9 megacities in the Greater Bay Area, China. A generalized linear model (GLM) was established to test the association between mobility volume (number of trips) and COVID-19 transmission. Subgroup analysis was also performed for sex, age, travel location, and travel distance. Statisticalinteractionterms were includedin a variety of models that express different relations between involved variables. The GLM analysis demonstrated a significant association between the COVID-19 growth rate ratio (GR) and mobility volume. A stratification analysis revealed a higher effect of mobility volume on the COVID-19 GR among people aged 50-59 years (GR decrease of 13.17% per 10% reduction in mobility volume; P<.001) than among other age groups (GR decreases of 7.80%, 10.43%, 7.48%, 8.01%, and 10.43% for those aged ≤18, 19-29, 30-39, 40-49, and ≥60 years, respectively; P=.02 for the interaction). The impact of mobility reduction on COVID-19 transmission was higher for transit stations and shopping areas (instantaneous reproduction number [Rt] decreases of 0.67 and 0.53 per 10% reduction in mobility volume, respectively) than for workplaces, schools, recreation areas, and other locations (Rt decreases of 0.30, 0.37, 0.44, and 0.32, respectively; P=.02 for the interaction). The association between mobility volume reduction and COVID-19 transmission was lower with decreasing mobility distance as there was a significant interaction between mobility volume and mobility distance with regard to Rt (P<.001 for the interaction). Specifically, the percentage decreases in Rt per 10% reduction in mobility volume were 11.97% when mobility distance increased by 10% (Spring Festival), 6.74% when mobility distance remained unchanged, and 1.52% when mobility distance declined by 10%. The association between mobility reduction and COVID-19 transmission significantly varied according to mobility distance, location, and age. The substantially higher impact of mobility volume on COVID-19 transmission for longer travel distance, certain age groups, and specific travel locations highlights the potential to optimize the effectiveness of mobility restriction strategies. The results from our study demonstrate the power of having a mobility network using mobile phone data for surveillance that can monitor movement at a detailed level to measure the potential impacts of future pandemics.

The role of absolute humidity in influenza transmission in Beijing, China: risk assessment and attributable fraction identification

ABSTRACT To assess the impact of absolute humidity on influenza transmission in Beijing from 2014 to 2019, we estimated the influenza transmissibility via the instantaneous reproduction number (Rt), and evaluated its nonlinear exposure-response association and delayed effects with absolute humidity by using the distributed lag nonlinear model (DLNM). Attributable fraction (AF) of Rt due to absolute humidity was calculated. The result showed a significant M-shaped relationship between Rt and absolute humidity. Compared with the effect of high absolute humidity, the low absolute humidity effect was more immediate with the most significant effect observed at lag 6 days. AFs were relatively high for the group aged 15–24 years, and was the lowest for the group aged 0–4 years with low absolute humidity. Therefore, we concluded that the component attributed to the low absolute humidity effect is greater. Young and middle-aged people are more sensitive to low absolute humidity than children and elderly.

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

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

The Impact of Urbanization and Human Mobility on Seasonal Influenza in Northern China.

The intensity of influenza epidemics varies significantly from year to year among regions with similar climatic conditions and populations. However, the underlying mechanisms of the temporal and spatial variations remain unclear. We investigated the impact of urbanization and public transportation size on influenza activity. We used 6-year weekly provincial-level surveillance data of influenza-like disease incidence (ILI) and viral activity in northern China. We derived the transmission potential of influenza for each epidemic season using the susceptible-exposed-infectious-removed-susceptible (SEIRS) model and estimated the transmissibility in the peak period via the instantaneous reproduction number (Rt). Public transport was found to explain approximately 28% of the variance in the seasonal transmission potential. Urbanization and public transportation size explained approximately 10% and 21% of the variance in maximum Rt in the peak period, respectively. For the mean Rt during the peak period, urbanization and public transportation accounted for 9% and 16% of the variance in Rt, respectively. Our results indicated that the differences in the intensity of influenza epidemics among the northern provinces of China were partially driven by urbanization and public transport size. These findings are beneficial for predicting influenza intensity and developing preparedness strategies for the early stages of epidemics.

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

This study investigates the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission potential in North Dakota, South Dakota, Montana, Wyoming, and Idaho from March 2020 through January 2021. Time-varying reproduction numbers, R t , of a 7-d-sliding-window and of non-overlapping-windows between policy changes were estimated using the instantaneous reproduction number method. Linear regression was performed to evaluate if per-capita cumulative case-count varied across counties with different population size or density. The median 7-d-sliding-window R t estimates across the studied region varied between 1 and 1.25 during September through November 2020. Between November 13 and 18, R t was reduced by 14.71% (95% credible interval, CrI, [14.41%, 14.99%]) in North Dakota following a mask mandate; Idaho saw a 1.93% (95% CrI [1.87%, 1.99%]) reduction and Montana saw a 9.63% (95% CrI [9.26%, 9.98%]) reduction following the tightening of restrictions. High-population and high-density counties had higher per-capita cumulative case-count in North Dakota on June 30, August 31, October 31, and December 31, 2020. In Idaho, North Dakota, South Dakota, and Wyoming, there were positive correlations between population size and per-capita weekly incident case-count, adjusted for calendar time and social vulnerability index variables. R t decreased after mask mandate during the region's case-count spike suggested reduction in SARS-CoV-2 transmission.

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

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