COVID-19 effective reproduction number determination: an application, and a review of issues and influential factors

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Luis Alfredo Bautista Balbás ◽  
Mario Gil Conesa ◽  
Blanca Bautista Balbás ◽  
Gil Rodríguez Caravaca
Keyword(s):  
Sensitivity Analysis ◽  
Web Application ◽  
Reproduction Number ◽  
Infected Individual ◽  
National Level ◽  
Conclusive Evidence ◽  
Influential Factors ◽  
Estimation Methods ◽  
Serial Interval ◽  
The Impact

Abstract Objectives An essential indicator of COVID-19 transmission is the effective reproduction number (R t ), the number of cases which an infected individual is expected to infect at a particular point in time; curves of the evolution of R t over time (transmission curves) reflect the impact of preventive measures and whether an epidemic is controlled. Methods We have created a Shiny/R web application (https://alfredob.shinyapps.io/estR0/) with user-selectable features: open data sources with daily COVID-19 incidences from all countries and many regions, customizable preprocessing options (smoothing, proportional increment, etc.), different MonteCarlo-Markov-Chain estimates of the generation time or serial interval distributions and state-of-the-art R t estimation frameworks (EpiEstim, R 0). This application could be used as a tool both to obtain transmission estimates and to perform interactive sensitivity analysis. We have analyzed the impact of these factors on transmission curves. We also have obtained curves at the national and sub-national level and analyzed the impact of epidemic control strategies, superspreading events, socioeconomic factors and outbreaks. Results Reproduction numbers showed earlier anticipation compared to active prevalence indicators (14-day cumulative incidence, overall infectivity). In the sensitivity analysis, the impact of different R t estimation methods was moderate/small, and the impact of different serial interval distributions was very small. We couldn’t find conclusive evidence regarding the impact of alleged superspreading events. As a limitation, dataset quality can limit the reliability of the estimates. Conclusions The thorough review of many examples of COVID-19 transmission curves support the usage of R t estimates as a robust transmission indicator.

scholarly journals COVID-19 effective reproductive ratio determination: An application, and analysis of issues and influential factors

2020 ◽  
Author(s):  
Luis Alfredo Bautista Balbás ◽  
Mario Gil Conesa ◽  
Gil Rodríguez Caravaca ◽  
Blanca Bautista Balbás
Keyword(s):  
Web Application ◽  
Control Strategies ◽  
Infected Individual ◽  
National Level ◽  
Open Data ◽  
Conclusive Evidence ◽  
Influential Factors ◽  
Mitigation Strategies ◽  
Epidemic Control ◽  
The Impact

An essential indicator of COVID-19 transmission is the effective reproduction number (Rt), the number of cases which an infected individual is expected to infect at a particular moment of time; curves of the evolution of Rt over time (transmission curves) reflect the impact of preventive measures and whether an epidemic is controlled. We have created a Shiny/R web application with user-selectable features: open data sources with daily COVID-19 incidences from all countries and many regions, customizable preprocessing options (smoothing, proportional increment, backwards distribution of negative corrections, etc), different MonteCarlo-Markov-Chain estimates of the generation time or serial interval distributions and state-of-the-art Rt estimation frameworks (EpiEstim, R0). We have analyzed the impact of these factors in the obtained transmission curves. We also have obtained curves at the national and sub-national level and analyzed the impact of epidemic control strategies, superspreading events, socioeconomic factors and outbreaks. We conclude that country wealth and, to a lesser extent, mitigation strategies, were associated with poorer epidemic control. Dataset quality was an important factor, and sometimes dictated the necessity of time series smoothing. We couldn't find conclusive evidence regarding the impact of alleged superspreading events. In the reopening phase, outbreaks had an impact on transmission curves. This application could be used interactively as a tool both to obtain transmission estimates and to perform interactive sensitivity analysis.

scholarly journals Early Transmission Dynamics of Novel Coronavirus (COVID-19) in Nigeria

2020 ◽  
Vol 17 (9) ◽  
pp. 3054 ◽  
Author(s):  
Oyelola A. Adegboye ◽  
Adeshina I. Adekunle ◽  
Ezra Gayawan
Keyword(s):  
Doubling Time ◽  
Reproduction Number ◽  
Infected Individual ◽  
Credible Interval ◽  
World Health ◽  
Time Interval ◽  
Serial Interval ◽  
Imported Cases ◽  
Novel Coronavirus ◽  
Health Organization

On 31 December 2019, the World Health Organization (WHO) was notified of a novel coronavirus disease in China that was later named COVID-19. On 11 March 2020, the outbreak of COVID-19 was declared a pandemic. The first instance of the virus in Nigeria was documented on 27 February 2020. This study provides a preliminary epidemiological analysis of the first 45 days of COVID-19 outbreak in Nigeria. We estimated the early transmissibility via time-varying reproduction number based on the Bayesian method that incorporates uncertainty in the distribution of serial interval (time interval between symptoms onset in an infected individual and the infector), and adjusted for disease importation. By 11 April 2020, 318 confirmed cases and 10 deaths from COVID-19 have occurred in Nigeria. At day 45, the exponential growth rate was 0.07 (95% confidence interval (CI): 0.05–0.10) with a doubling time of 9.84 days (95% CI: 7.28–15.18). Separately for imported cases (travel-related) and local cases, the doubling time was 12.88 days and 2.86 days, respectively. Furthermore, we estimated the reproduction number for each day of the outbreak using a three-weekly window while adjusting for imported cases. The estimated reproduction number was 4.98 (95% CrI: 2.65–8.41) at day 22 (19 March 2020), peaking at 5.61 (95% credible interval (CrI): 3.83–7.88) at day 25 (22 March 2020). The median reproduction number over the study period was 2.71 and the latest value on 11 April 2020, was 1.42 (95% CrI: 1.26–1.58). These 45-day estimates suggested that cases of COVID-19 in Nigeria have been remarkably lower than expected and the preparedness to detect needs to be shifted to stop local transmission.

scholarly journals Are we there yet? An adaptive SIR model for continuous estimation of COVID-19 infection rate and reproduction number in the United States (Preprint)

2020 ◽  
Author(s):  
Mark Shapiro ◽  
Fazle Karim ◽  
Guido Muscioni ◽  
Abel Saju Augustine
Keyword(s):  
Infection Rate ◽  
Reproduction Number ◽  
Infected Individual ◽  
Local Population ◽  
The United States ◽  
Mitigation Measures ◽  
Simple Method ◽  
Wide Range ◽  
Continuous Estimation ◽  
The Impact

BACKGROUND The dynamics of the COVID-19 epidemic vary due to local population density and policy measures. When making decisions, policy makers consider an estimate of the effective reproduction number R_t which is the expected number of secondary infections by a single infected individual. OBJECTIVE We propose a simple method for estimating the time-varying infection rate and reproduction number R_t . METHODS We use a sliding window approach applied to a Susceptible-Infectious-Removed model. The infection rate is estimated using the reported cases for a seven-day window to obtain continuous estimation of R_t. The proposed adaptive SIR (aSIR) model was applied to data at the state and county levels. RESULTS The aSIR model showed an excellent fit for the number of reported COVID-19 positive cases, a one-day forecast MAPE was less than 2.6% across all states. However, a seven-day forecast MAPE reached 16.2% and strongly overestimated the number of cases when the reproduction number was high and changing fast. The maximal R_t showed a wide range of 2.0 to 4.5 across all states, with the highest values for New York (4.4) and Michigan (4.5). We demonstrate that the aSIR model can quickly adapt to an increase in the number of tests and associated increase in the reported cases of infections. Our results also suggest that intensive testing may be one of the effective methods of reducing R_t. CONCLUSIONS The aSIR model provides a simple and accurate computational tool to obtain continuous estimation of the reproduction number and evaluate the impact of mitigation measures.

scholarly journals Meta-analysis of the SARS-CoV-2 serial interval and the impact of parameter uncertainty on the COVID-19 reproduction number

2020 ◽  
Author(s):  
Robert Challen ◽  
Ellen Brooks-Pollock ◽  
Krasimira Tsaneva-Atanasova ◽  
Leon Danon
Keyword(s):  
Incubation Period ◽  
Time Delays ◽  
Hospital Admissions ◽  
Reproduction Number ◽  
Meta Analysis ◽  
Model Parameters ◽  
Small Data ◽  
Generation Interval ◽  
Serial Interval ◽  
The Impact

AbstractThe serial interval of an infectious disease, commonly interpreted as the time between onset of symptoms in sequentially infected individuals within a chain of transmission, is a key epidemiological quantity involved in estimating the reproduction number. The serial interval is closely related to other key quantities, including the incubation period, the generation interval (the time between sequential infections) and time delays between infection and the observations associated with monitoring an outbreak such as confirmed cases, hospital admissions and deaths. Estimates of these quantities are often based on small data sets from early contact tracing and are subject to considerable uncertainty, which is especially true for early COVID-19 data. In this paper we estimate these key quantities in the context of COVID-19 for the UK, including a meta-analysis of early estimates of the serial interval. We estimate distributions for the serial interval with a mean 5.6 (95% CrI 5.1–6.2) and SD 4.2 (95% CrI 3.9–4.6) days (empirical distribution), the generation interval with a mean 4.8 (95% CrI 4.3–5.41) and SD 1.7 (95% CrI 1.0–2.6) days (fitted gamma distribution), and the incubation period with a mean 5.5 (95% CrI 5.1–5.8) and SD 4.9 (95% CrI 4.5–5.3) days (fitted log normal distribution). We quantify the impact of the uncertainty surrounding the serial interval, generation interval, incubation period and time delays, on the subsequent estimation of the reproduction number, when pragmatic and more formal approaches are taken. These estimates place empirical bounds on the estimates of most relevant model parameters and are expected to contribute to modelling COVID-19 transmission.

scholarly journals An Examination of the Determination of Medical Capacity under a National Health Insurance Program

2019 ◽  
Vol 16 (7) ◽  
pp. 1206
Author(s):  
Yi-Tui Chen
Keyword(s):  
Sensitivity Analysis ◽  
Theoretical Analysis ◽  
Positive Impact ◽  
National Level ◽  
Medical Expenditure ◽  
Private Goods ◽  
Insurance Program ◽  
The Government ◽  
The Impact

This paper examines the capacity determination factors of medical services at a national level through the analysis of a mathematical model that maximizes social welfare, which consists of the consumption of private goods and the medical capacity provided by the society. A sensitivity analysis is conducted to investigate the impact of these factors on the medical capacity provided. Furthermore, a case example based on the data provided by the government is presented to discuss the results derived from the theoretical analysis. The results of the sensitivity analysis indicate that individual disposable income, the medical expenditure for each treatment, the level of premium payments, and substitution parameters have a positive impact on medical capacity, while the medical costs and preference parameter negatively affect medical capacity. The results of the correlation analysis based on the data of the case example are consistent with the findings of the theoretical analysis.

scholarly journals The Importance of Prior Sensitivity Analysis in Bayesian Statistics: Demonstrations Using an Interactive Shiny App

2020 ◽  
Vol 11 ◽  
Author(s):  
Sarah Depaoli ◽  
Sonja D. Winter ◽  
Marieke Visser
Keyword(s):  
Sensitivity Analysis ◽  
Simulation Study ◽  
Bayesian Methods ◽  
Multiple Regression Model ◽  
Specific Model ◽  
Estimation Methods ◽  
Prior Distributions ◽  
Shiny App ◽  
Novice Users ◽  
The Impact

The current paper highlights a new, interactive Shiny App that can be used to aid in understanding and teaching the important task of conducting a prior sensitivity analysis when implementing Bayesian estimation methods. In this paper, we discuss the importance of examining prior distributions through a sensitivity analysis. We argue that conducting a prior sensitivity analysis is equally important when so-called diffuse priors are implemented as it is with subjective priors. As a proof of concept, we conducted a small simulation study, which illustrates the impact of priors on final model estimates. The findings from the simulation study highlight the importance of conducting a sensitivity analysis of priors. This concept is further extended through an interactive Shiny App that we developed. The Shiny App allows users to explore the impact of various forms of priors using empirical data. We introduce this Shiny App and thoroughly detail an example using a simple multiple regression model that users at all levels can understand. In this paper, we highlight how to determine the different settings for a prior sensitivity analysis, how to visually and statistically compare results obtained in the sensitivity analysis, and how to display findings and write up disparate results obtained across the sensitivity analysis. The goal is that novice users can follow the process outlined here and work within the interactive Shiny App to gain a deeper understanding of the role of prior distributions and the importance of a sensitivity analysis when implementing Bayesian methods. The intended audience is broad (e.g., undergraduate or graduate students, faculty, and other researchers) and can include those with limited exposure to Bayesian methods or the specific model presented here.

scholarly journals Trajectory of individual immunity and vaccination required for SARS-CoV-2 community immunity: a conceptual investigation

2021 ◽  
Vol 18 (175) ◽  
pp. 20200683
Author(s):  
Chadi M. Saad-Roy ◽  
Simon A. Levin ◽  
C. Jessica E. Metcalf ◽  
Bryan T. Grenfell
Keyword(s):  
Reproduction Number ◽  
Infected Individual ◽  
Mitigation Measures ◽  
Simple Description ◽  
Vaccination Rates ◽  
Epidemic Dynamics ◽  
Low Levels ◽  
Analytical Relations ◽  
The Impact ◽  
Individual Immunity

SARS-CoV-2 is an international public health emergency; high transmissibility and morbidity and mortality can result in the virus overwhelming health systems. Combinations of social distancing, and test, trace, and isolate strategies can reduce the number of new infections per infected individual below 1, thus driving declines in case numbers, but may be both challenging and costly. These interventions must also be maintained until development and (now likely) mass deployment of a vaccine (or therapeutics), since otherwise, many susceptible individuals are still at risk of infection. We use a simple analytical model to explore how low levels of infection, combined with vaccination, determine the trajectory to community immunity. Understanding the repercussions of the biological characteristics of the viral life cycle in this scenario is of considerable importance. We provide a simple description of this process by modelling the scenario where the effective reproduction number R eff is maintained at 1. Since the additional complexity imposed by the strength and duration of transmission-blocking immunity is not yet clear, we use our framework to probe the impact of these uncertainties. Through intuitive analytical relations, we explore how the necessary magnitude of vaccination rates and mitigation efforts depends crucially on the durations of natural and vaccinal immunity. We also show that our framework can encompass seasonality or preexisting immunity due to epidemic dynamics prior to strong mitigation measures. Taken together, our simple conceptual model illustrates the importance of individual and vaccinal immunity for community immunity, and that the quantification of individuals immunized against SARS-CoV-2 is paramount.

scholarly journals Novel Coronavirus in Nigeria: Epidemiological analysis of the first 45 days of the pandemic

2020 ◽  
Author(s):  
Oyelola A. Adegboye ◽  
Adeshina I. Adekunle ◽  
Ezra Gayawan
Keyword(s):  
Doubling Time ◽  
Reproduction Number ◽  
Infected Individual ◽  
World Health ◽  
Time Interval ◽  
Epidemiological Analysis ◽  
Serial Interval ◽  
Novel Coronavirus ◽  
Health Organization ◽  
Local Transmission

AbstractBackgroundOn December 31, 2019, the World Health Organization (WHO) was notified of a novel coronavirus in China that was later named COVID-19. On March 11, 2020, the outbreak of COVID-19 was declared a pandemic. The first instance of the virus in Nigeria was documented on February 27, 2020.MethodsThis study provides a preliminary epidemiological analysis of the first 45 days of COVID-19 outbreak in Nigeria quantifying. We estimated the early transmissibility via time-varying reproduction number based on Bayesian method that incorporates uncertainty in the distribution of serial interval (time interval between symptoms onset in an infected individual and the infector) and adjusted for disease importation.FindingsBy April 11, 2020, 318 confirmed cases and 10 deaths from COVID-19 have occurred in Nigeria. At day 45, the exponential growth rate was 0.07 (95% Confidence Interval (CI): 0.05 – 0.10) with doubling time of 9.84 days (95% CI: 7.28 – 15.18). Separately for travel related and local cases the doubling time was 12.88 days and 2.86 days, respectively. Furthermore, we estimated the reproduction number for each day of the outbreak using three-weekly window while adjusting for travel related cases. The estimated reproduction number was 4.98 (95% CrI: 2.65 – 8.41) at day 22 (March 19, 2020), peaking at 5.61 (95% CrI: 3.83 –7.88) at day 25 (March 22, 2020). The median reproduction number over the study period was 2.71 and the latest value at April 11, 2020 was 1.42 (95% CI: 1.26 – 1.58).InterpretationThese 45-day estimates suggested that cases of COVID-19 in Nigeria have been remarkably lower than expected and the preparedness to detect needs to be shifted to stop local transmission.FundingNone

scholarly journals How do interventions impact malaria dynamics between neighboring countries? A case study with Botswana and Zimbabwe

2019 ◽  
Author(s):  
Folashade Agusto ◽  
Amy Goldberg ◽  
Omayra Ortega ◽  
Joan Ponce ◽  
Sofya Zaytseva ◽  
...  
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Human Mobility ◽  
National Level ◽  
The Other ◽  
Disease Dynamics ◽  
The World ◽  
Vector Borne ◽  
The Impact

AbstractMalaria is a vector-borne disease that is responsible for over 400,000 deaths per year. Although countries around the world have taken measures to decrease the incidence of malaria, many regions remain endemic. Indeed, progress towards elimination has stalled in multiple countries. While control efforts are largely focused at the national level, the movement of individuals between countries may complicate the efficacy of elimination efforts. Here, we consider the case of neighboring countries Botswana and Zimbabwe, connected by human mobility. Both have improved malaria rates in recent years with differing success. We use a two-patch Ross-MacDonald Model with Lagrangian human mobility to examine the coupled disease dynamics between these two countries. In particular, we are interested in the impact that interventions for controlling malaria applied in one country can have on the incidence of malaria in the other country. We find that dynamics and interventions in Zimbabwe can dramatically influence pathways to elimination in Botswana, largely driven by Zimbabwe’s population size and larger basic reproduction number.

scholarly journals Evaluation of Environmental Impact of Car Sharing in Consideration of Uncertainty of Influential Variables

2020 ◽  
Vol 14 (6) ◽  
pp. 975-983
Author(s):  
Katsuya Tsuji ◽  
◽  
Kiyo Kurisu ◽  
Jun Nakatani ◽  
Yuichi Moriguchi
Keyword(s):  
Sensitivity Analysis ◽  
Service Providers ◽  
Rebound Effect ◽  
Environmentally Friendly ◽  
Sharing Economy ◽  
Influential Factors ◽  
Car Sharing ◽  
New Production ◽  
Rebound Effects ◽  
The Impact

Sustainable production and consumption are categorized as target 12 in the United Nations’ Sustainable Development Goals. The “sharing economy” has been developing globally as a new consumption style, and it is often recognized as being environmentally friendly by both consumers and service providers. Several aspects of the practice, such as the avoidance of new production, can reduce the impact to the environment. However, additional factors, such as the expansion of consumption, namely rebound effects, can increase the impact to the environment. Although many variables exist to determine the total impact of sharing services on the environment, additional and rebound effects and the uncertainty of influential variables have not been well considered. In this study, we aim to reveal the conditions that car-sharing practices place in increasing or decreasing environmental loads, and to identify the significant influential factors on the environment imposed by car-sharing services. We analyze the CO2 emission of car sharing by considering various influential factors and their distributions. Furthermore, we consider differences in car size, fuel type, ownership condition, and several other factors in the simulation. The distribution of each variable is determined, and a Monte Carlo simulation is conducted. The CO2 emissions from the production and operational stages over a 10-y period are estimated. The simulation is conducted with sensitivity analysis to identify the variables that contribute significantly to the total CO2 emission. In some cases, the CO2 emission involved in car sharing exceeded cases in which car sharing is not practiced. Among those cases, although the main contributor to the total CO2 emission is in the operational stage, CO2 emission from the production stage increased the amount of emission. It is discovered that the number of cars increased significantly during the target 10 y after sharing is introduced in some cases. These results indicate a high probability that car sharing can achieve CO2 reduction, but the increase in CO2 emission can occur under certain conditions. Additionally, the sensitivity analysis shows that the main determinants of CO2 emission are the ratio of people who eliminated their private cars, degree of rebound effect, and increasing ratio of number of cars introduced to car-sharing practices. This suggests that whether car sharing becomes environmentally friendly depends substantially on consumer behavior and the manner in which sharing services are operated.

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