Estimation of Time-Dependent Reproduction Number for Global COVID-19 Outbreak

Real-time estimation of the parameters characterising infectious disease transmission is important for optimization quarantine interventions during outbreaks. One of the most significant parameters is the effective reproduction number - number of secondary cases produced by a single infection. The current study presents an approach for estimating the effective reproduction number and its application to COVID-19 outbreak. The method is based on fitting SIR epidemic model to observation data in a sliding time window and allows to show real-time dynamics of reproduction number at any phase of epidemic for countries globally. Online data on COVID-19 daily cases of infections, recoveries, deaths are used.Finally, time-dependent reproduction number is explored in connection with dynamics of peoples mobility. The method allows to assess the disease transmission potential and understand the effect of interventions on epidemics spread. It also can be easily adapted to future outbreaks of different pathogens. The tool is available online as Python code from the Github repository.

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Real-time estimation of time-dependent imposed heat flux in graded index media by KF-RLSE algorithm

Applied Thermal Engineering ◽

10.1016/j.applthermaleng.2018.12.170 ◽

2019 ◽

Vol 150 ◽

pp. 1-10 ◽

Cited By ~ 6

Author(s):

Shuang Wen ◽

Hong Qi ◽

Xiao-Ying Yu ◽

Ya-Tao Ren ◽

Lin-Yang Wei ◽

...

Keyword(s):

Heat Flux ◽

Real Time ◽

Time Estimation ◽

Time Dependent ◽

Graded Index ◽

Real Time Estimation ◽

Estimation Of Time

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Real Time Dynamics of Hole Propagation in Strongly Correlated Conjugated Molecular Chains: A time-dependent DMRG Study

Computing Letters ◽

10.1163/157404007782913219 ◽

2007 ◽

Vol 3 (2) ◽

pp. 457-472 ◽

Cited By ~ 4

Author(s):

Tirthankar Dutta ◽

Ramasesha

Keyword(s):

Real Time ◽

Time Dependent ◽

Strongly Correlated ◽

Time Dynamics

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Estimation of the Time-dependent Reproduction Number of Influenza A(H1N1)pdm2009 in South Korea

10.21203/rs.3.rs-20387/v1 ◽

2020 ◽

Author(s):

Yunjeong Lee ◽

Dong Han Lee ◽

Hee-Dae Kwon ◽

Changsoo Kim ◽

Jeehyun Lee

Keyword(s):

South Korea ◽

Influenza A ◽

Reproduction Number ◽

Time Estimation ◽

Time Dependent ◽

Estimation Of Parameters ◽

Transmission Potential ◽

Reproduction Numbers ◽

Influenza A H1n1 ◽

Feasible Range

Abstract Background: The reproduction number is one of the most crucial parameters in determining disease dynamics, providing a summary measure of the transmission potential. However, estimating this value is particularly challenging owing to the characteristics of epidemic data, including non-reproducibility and incompleteness.Methods: In this study, we propose mathematical models with different population structures; each of these models can produce data on the number of cases of the influenza A(H1N1)pdm09 epidemic in South Korea. These structured models incorporating the heterogeneity of age and region are used to estimate the time-dependent effective reproduction numbers. Subsequently, the age- and region-specific reproduction numbers are also computed to analyze the differences illustrated in the incidence data.Results: The basic SIR fails to provide a reasonable estimation of the reproduction numbers. The estimated values demonstrate a large variation and remains outside of the feasible range for the influenza, regardless of the time period for data. Real-time estimation using age- and region-structured models demonstrated that the effective reproduction number rose sharply during mid-October when the ㅜumber of patients increased dramatically. The reproduction number fell below unity at the end of October and stayed lower than unity indicating that the epidemic starts decreasing, which is consistent with the incidence data.Conclusions: Numerical results reveal that the introduction of heterogeneity into the population to represent the general characteristics of dynamics is essential for the robust estimation of parameters.

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TW-SIR: Time-window based SIR for COVID-19 forecasts

10.21203/rs.3.rs-75220/v1 ◽

2020 ◽

Author(s):

Zhifang Liao ◽

Peng Lan ◽

Zhingning Liao ◽

Yan Zhang ◽

Shengzong Liu

Keyword(s):

Real Time ◽

Reproduction Number ◽

Time Window ◽

Data Sets ◽

Machine Learning Method ◽

The Real ◽

Multiple Data ◽

Multiple Data Sets ◽

Time Changes ◽

Epidemic Diseases

Abstract Since the outbreak of COVID-19, many COVID-19 research studies have proposed different models for predicting trend of COVID-19. Among them, the prediction model based on mathematical epidemiology (SIR) is the most widely used, but most of these models are adapted in special situations based on various assumptions. In order to reflect the real-time trend of the epidemic in the process of infection for different areas, different policies and different epidemic diseases, a general adapted time- window based SIR model is proposed, which is characterized by introducing a time window mechanism for dynamic data analysis and using machine learning method predicts the Basic reproduction number R0 and the exponential growth rate of the epidemic. Multiple data sets of epidemic diseases are analyzed, and the numerical results showed that the framework can effectively measure the real-time changes of the parameters during the epidemic, and error rate of predicting the number of COVID-19 infections in a single day is within 5%

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China’s effective control and other countries’ uncharted challenge against COVID-19: an epidemiological and modelling study

10.1101/2020.04.28.20083899 ◽

2020 ◽

Author(s):

Lingling Zheng ◽

Qin Kang ◽

Weiyao Liao ◽

Xiujuan Chen ◽

Shuai Huang ◽

...

Keyword(s):

Disease Transmission ◽

Reproduction Number ◽

Case Reports ◽

Epidemiological Data ◽

Control Measures ◽

Time Dependent ◽

Effective Control ◽

List Type ◽

Global Epidemic ◽

Serial Interval

AbstractBackgroundOn the present trajectory, COVID is inevitably becoming a global epidemic, leading to concerns regarding the pandemic potential in China and other countries.ObjectiveIn this study, we use the time-dependent reproduction number (Rt) to comprise the COVID transmissibility across different countries.MethodsWe used data from Jan 20, 2019, to Feb 29, 2020, on the number of newly confirmed cases, obtained from the reports published by the CDC, to infer the incidence of infectious over time. A two-step procedure was used to estimate the Rt. The first step used data on known index-secondary cases pairs, from publicly available case reports, to estimate the serial interval distribution. The second step estimated the Rt jointly from the incidence data and the information data in the first step. Rt was then used to simulate the epidemics across all major cities in China and typical countries worldwide.ResultsBased on a total of 126 index-secondary cases pairs from 4 international regions, we estimated that the serial interval for SARS-2-CoV was 4.18 (IQR 1.92 – 6.65) days. Domestically, Rt of China, Hubei province, Wuhan had fallen below 1.0 on 9 Feb, 10 Feb and 13 Feb (Rt were 0.99±0.02, 0.99±0.02 and 0.96±0.02), respectively. Internationally, as of 26 Feb, statistically significant periods of COVID spread (Rt >1) were identified for most regions, except for Singapore (Rt was 0.92±0.17).ConclusionsThe epidemic in China has been well controlled, but the worldwide pandemic has not been well controlled. Worldwide preparedness and vulnerability against COVID-19 should be regarded with more care.What is already known on this subject?The basic reproduction number (R0) and the-time-dependent reproduction number (Rt) are two important indicators of infectious disease transmission. In addition, Rt as a derivative of R0 could be used to assess the epidemiological development of the disease and effectiveness of control measures. Most current researches used data from earlier periods in Wuhan and refer to the epidemiological features of SARS, which are possibly biased. Meanwhile, there are fewer studies discussed the Rt of COVID-19. Current clinical and epidemiological data are insufficient to help us understand the full view of the potential transmission of this disease.What this study adds?We use up-to-data observation of the serial interval and cases arising from local transmission to calculate the Rt in different outbreak level area and every province in China as well as five-top sever outbreak countries and other overseas. By comparing the Rt, we discussed the situation of outbreak around the world.

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Real-Time Estimation of Rt for Supporting Public-Health Policies Against COVID-19

Frontiers in Public Health ◽

10.3389/fpubh.2020.556689 ◽

2020 ◽

Vol 8 ◽

Author(s):

Sebastián Contreras ◽

H. Andrés Villavicencio ◽

David Medina-Ortiz ◽

Claudia P. Saavedra ◽

Álvaro Olivera-Nappa

Keyword(s):

Public Health ◽

Real Time ◽

Reproduction Number ◽

Case Reports ◽

Mathematical Formulation ◽

Time Estimation ◽

Consensus Protocol ◽

Viral Spread ◽

Effective Interventions ◽

Secondary Infections

In the absence of a consensus protocol to slow down the spread of SARS-CoV-2, policymakers need real-time indicators to support decisions in public health matters. The Effective Reproduction Number (Rt) represents the number of secondary infections generated per each case and can be dramatically modified by applying effective interventions. However, current methodologies to calculate Rt from data remain somewhat cumbersome, thus raising a barrier between its timely calculation and application by policymakers. In this work, we provide a simple mathematical formulation for obtaining the effective reproduction number in real-time using only and directly daily official case reports, obtained by modifying the equations describing the viral spread. We numerically explore the accuracy and limitations of the proposed methodology, which was demonstrated to provide accurate, timely, and intuitive results. We illustrate the use of our methodology to study the evolution of the pandemic in different iconic countries, and to assess the efficacy and promptness of different public health interventions.

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Practical considerations for measuring the effective reproductive number, Rt

PLoS Computational Biology ◽

10.1371/journal.pcbi.1008409 ◽

2020 ◽

Vol 16 (12) ◽

pp. e1008409

Author(s):

Katelyn M. Gostic ◽

Lauren McGough ◽

Edward B. Baskerville ◽

Sam Abbott ◽

Keya Joshi ◽

...

Keyword(s):

Real Time ◽

Disease Transmission ◽

Synthetic Data ◽

Time Estimation ◽

Reproductive Number ◽

Open Problems ◽

Empirical Estimates ◽

Public Health Officials ◽

Real Time Estimation ◽

The Moment

Estimation of the effective reproductive number Rt is important for detecting changes in disease transmission over time. During the Coronavirus Disease 2019 (COVID-19) pandemic, policy makers and public health officials are using Rt to assess the effectiveness of interventions and to inform policy. However, estimation of Rt from available data presents several challenges, with critical implications for the interpretation of the course of the pandemic. The purpose of this document is to summarize these challenges, illustrate them with examples from synthetic data, and, where possible, make recommendations. For near real-time estimation of Rt, we recommend the approach of Cori and colleagues, which uses data from before time t and empirical estimates of the distribution of time between infections. Methods that require data from after time t, such as Wallinga and Teunis, are conceptually and methodologically less suited for near real-time estimation, but may be appropriate for retrospective analyses of how individuals infected at different time points contributed to the spread. We advise caution when using methods derived from the approach of Bettencourt and Ribeiro, as the resulting Rt estimates may be biased if the underlying structural assumptions are not met. Two key challenges common to all approaches are accurate specification of the generation interval and reconstruction of the time series of new infections from observations occurring long after the moment of transmission. Naive approaches for dealing with observation delays, such as subtracting delays sampled from a distribution, can introduce bias. We provide suggestions for how to mitigate this and other technical challenges and highlight open problems in Rt estimation.

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Practical considerations for measuring the effective reproductive number, Rt

10.1101/2020.06.18.20134858 ◽

2020 ◽

Cited By ~ 18

Author(s):

Katelyn M. Gostic ◽

Lauren McGough ◽

Ed Baskerville ◽

Sam Abbott ◽

Keya Joshi ◽

...

Keyword(s):

Real Time ◽

Disease Transmission ◽

Synthetic Data ◽

Time Estimation ◽

Reproductive Number ◽

Open Problems ◽

Empirical Estimates ◽

Public Health Officials ◽

Real Time Estimation ◽

The Moment

AbstractEstimation of the effective reproductive number, Rt, is important for detecting changes in disease transmission over time. During the COVID-19 pandemic, policymakers and public health officials are using Rt to assess the effectiveness of interventions and to inform policy. However, estimation of Rt from available data presents several challenges, with critical implications for the interpretation of the course of the pandemic. The purpose of this document is to summarize these challenges, illustrate them with examples from synthetic data, and, where possible, make methodological recommendations. For near real-time estimation of Rt, we recommend the approach of Cori et al. (2013), which uses data from before time t and empirical estimates of the distribution of time between infections. Methods that require data from after time t, such as Wallinga and Teunis (2004), are conceptually and methodologically less suited for near real-time estimation, but may be appropriate for some retrospective analyses. We advise against using methods derived from Bettencourt and Ribeiro (2008), as the resulting Rt estimates may be biased if the underlying structural assumptions are not met. A challenge common to all approaches is reconstruction of the time series of new infections from observations occurring long after the moment of transmission. Naive approaches for dealing with observation delays, such as subtracting delays sampled from a distribution, can introduce bias. We provide suggestions for how to mitigate this and other technical challenges and highlight open problems in Rt estimation.

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An Optimization Method of Time Window Based on Travel Time and Reliability

Mathematical Problems in Engineering ◽

10.1155/2015/921480 ◽

2015 ◽

Vol 2015 ◽

pp. 1-9

Author(s):

Fengjie Fu ◽

Dongfang Ma ◽

Dianhai Wang ◽

Wei Qian

Keyword(s):

Travel Time ◽

Real Time ◽

Time Window ◽

Time Windows ◽

Time Estimation ◽

Optimization Method ◽

Time Change ◽

Basic Unit ◽

Optimal Time ◽

Travel Time Estimation

The dynamic change of urban road travel time was analyzed using video image detector data, and it showed cyclic variation, so the signal cycle length at the upstream intersection was conducted as the basic unit of time window; there was some evidence of bimodality in the actual travel time distributions; therefore, the fitting parameters of the travel time bimodal distribution were estimated using the EM algorithm. Then the weighted average value of the two means was indicated as the travel time estimation value, and the Modified Buffer Time Index (MBIT) was expressed as travel time variability; based on the characteristics of travel time change and MBIT along with different time windows, the time window was optimized dynamically for minimum MBIT, requiring that the travel time change be lower than the threshold value and traffic incidents can be detected real time; finally, travel times on Shandong Road in Qingdao were estimated every 10 s, 120 s, optimal time windows, and 480 s and the comparisons demonstrated that travel time estimation in optimal time windows can exactly and steadily reflect the real-time traffic. It verifies the effectiveness of the optimization method.

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