The Acceleration Index as a Test-Controlled Reproduction Number: Application to COVID-19 in France*

AbstractWe show that the acceleration index, a novel indicator that measures acceleration and deceleration of viral spread (Baunez et al. 2020a,b), is essentially a test-controlled version of the reproduction number. As such it is a more accurate indicator to track the dynamics of an infectious disease outbreak in real time. We indicate a discrepancy between the acceleration index and the reproduction number, based on the infectivity and test rates and we provide a formal decomposition of this difference. When applied to French data for the ongoing COVID-19 pandemic, our decomposition shows that the reproduction number consistenly underestimates the resurgence of the pandemic since the summer of 2020, compared to the acceleration index which accounts for the time-varying volume of tests. From the comparison that we present here follows that the acceleration index is a sufficient statistic to track the pandemic’s propagation, as it captures in real time the sizeable time variation featured by viral circulation.JEL Classification NumbersI18; H12

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Estimation of the Time-Varying Reproduction Number of COVID-19 Outbreak in China

10.1101/2020.02.08.20021253 ◽

2020 ◽

Cited By ~ 31

Author(s):

Chong You ◽

Yuhao Deng ◽

Wenjie Hu ◽

Jiarui Sun ◽

Qiushi Lin ◽

...

Keyword(s):

Standard Deviation ◽

World Wide ◽

Reproduction Number ◽

Infectious Period ◽

Time Varying ◽

Exponential Growth Rate ◽

Reproduction Numbers ◽

Serial Interval ◽

Controlled Reproduction ◽

Novel Coronavirus

BackgroundThe 2019-nCoV outbreak in Wuhan, China has attracted world-wide attention. As of February 11, 2020, a total of 44730 cases of novel coronavirus-infected pneumonia associated with COVID-19 were confirmed by the National Health Commission of China.MethodsThree approaches, namely Poisson likelihood-based method (ML), exponential growth rate-based method (EGR) and stochastic Susceptible-Infected-Removed dynamic model-based method (SIR), were implemented to estimate the basic and controlled reproduction numbers.ResultsA total of 71 chains of transmission together with dates of symptoms onset and 67 dates of infections were identified among 5405 confirmed cases outside Hubei as reported by February 2, 2020. Based on this information, we find the serial interval having an average of 4.41 days with a standard deviation of 3.17 days and the infectious period having an average of 10.91 days with a standard deviation of 3.95 days.ConclusionsThe controlled reproduction number is declining. It is lower than one in most regions of China, but is still larger than one in Hubei Province. Sustained efforts are needed to further reduce the Rc to below one in order to end the current epidemic.

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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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A Modeling Study on the Estimation of COVID-19 Daily and Weekly Cases and Reproduction Number Using the Adaptive Kalman Filter: The Example of Ziraat Bank, Turkey

10.47260/jsem/1032 ◽

2021 ◽

pp. 15-27

Author(s):

İlker Met ◽

Levent Özbek ◽

Himmet Aksoy ◽

Ayfer Erkoç

Keyword(s):

Time Series ◽

Kalman Filter ◽

Reproduction Number ◽

Jel Classification ◽

Model Parameters ◽

Time Varying ◽

Adaptive Kalman Filter ◽

Human Race ◽

Time Varying Parameter ◽

Case Number

Abstract Since the beginning of 2020, the world has been struggling with a viral epidemic (COVID-19), which poses a serious threat to the collective health of the human race. Mathematical modeling of epidemics is critical for developing such policies, especially during these uncertain times. In this study, the reproduction number and model parameters were predicted using AR(1) (autoregressive time-series model of order 1) and the adaptive Kalman filter (AKF). The data sample used in the study consists of the weekly and daily number of cases amongst the Ziraat Bank personnel between March 11, 2020, and April 19, 2021. This sample was modeled in the state space, and the AKF was used to estimate the number of cases per day. It is quite simple to model the daily and weekly case number time series with the time-varying parameter AR(1) stochastic process and to estimate the time-varying parameter with online AKF. Overall, we found that the weekly case number prediction was more accurate than the daily case number (R2 = 0.97), especially in regions with a low number of cases. We suggest that the simplest method for reproduction number estimation can be obtained by modeling the daily cases using an AR(1) model. JEL classification numbers: C02, C22, C32. Keywords: COVID-19, Modeling, Reproduction number estimation, AR(1), Kalman filter.

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Improved estimation of time-varying reproduction numbers at low case incidence and between epidemic waves

10.1101/2020.09.14.20194589 ◽

2020 ◽

Cited By ~ 1

Author(s):

Kris Varun Parag

Keyword(s):

Real Time ◽

Change Point ◽

Reproduction Number ◽

Window Size ◽

Time Varying ◽

Markov State ◽

State Process ◽

Reproduction Numbers ◽

Low Incidence ◽

Estimation Of Time

We construct a recursive Bayesian smoother, termed EpiFilter, for estimating the effective reproduction number, R, from the incidence of an infectious disease in real time and retrospectively. Our approach borrows from Kalman filtering theory, is quick and easy to compute, generalisable, deterministic and unlike many current methods, requires no change-point or window size assumptions. We model R as a flexible, hidden Markov state process and exactly solve forward-backward algorithms, to derive R estimates that incorporate all available incidence information. This unifies and extends two popular methods, EpiEstim, which considers past incidence, and the Wallinga-Teunis method, which looks forward in time. This combination of maximising information and minimising assumptions, makes EpiFilter more statistically robust in periods of low incidence, where existing methods can struggle. As a result, we find EpiFilter to be particularly suited for assessing the risk of second waves of infection, in real time.

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EpiLPS: a fast and flexible Bayesian tool for near real-time estimation of the time-varying reproduction number

10.1101/2021.12.02.21267189 ◽

2021 ◽

Author(s):

Oswaldo Gressani ◽

Jacco Wallinga ◽

Christian Althaus ◽

Niel Hens ◽

Christel Faes

Keyword(s):

Real Time ◽

Negative Binomial ◽

Reproduction Number ◽

Time Estimation ◽

Renewal Equation ◽

Closed Form Expression ◽

Time Varying ◽

Epidemic Curve ◽

Influenza A H1n1 ◽

Real Time Estimation

AbstractIn infectious disease epidemiology, the instantaneous reproduction number R(t) is a timevarying metric defined as the average number of secondary infections generated by individuals who are infectious at time t. It is therefore a crucial epidemiological parameter that assists public health decision makers in the management of an epidemic. We present a new Bayesian tool 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 envelopes of R(t) 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 R(t) in only a few seconds; and (2) an approach based on a 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 excess variability 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 R(t) 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 current SARS-CoV-2 pandemic (2020-2021) for Belgium, Portugal, Denmark and France.Author summaryThe instantaneous reproduction number R(t) is a key metric that provides important insights into an epidemic outbreak. We present a flexible Bayesian approach called EpiLPS (Epidemiological modeling with Laplacian-P-splines) for smooth estimation of the epidemic curve and R(t). Computational speed and absence of arbitrary assumptions on smoothing makes EpiLPS an interesting tool for near real-time estimation of the reproduction number. An R software package is available (https://github.com/oswaldogressani).

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Improved estimation of time-varying reproduction numbers at low case incidence and between epidemic waves

PLoS Computational Biology ◽

10.1371/journal.pcbi.1009347 ◽

2021 ◽

Vol 17 (9) ◽

pp. e1009347

Author(s):

Kris V. Parag

Keyword(s):

Real Time ◽

Reproduction Number ◽

Spatial Scales ◽

Window Size ◽

Time Varying ◽

Markov State ◽

State Process ◽

Reproduction Numbers ◽

Low Incidence ◽

Estimation Of Time

We construct a recursive Bayesian smoother, termed EpiFilter, for estimating the effective reproduction number, R, from the incidence of an infectious disease in real time and retrospectively. Our approach borrows from Kalman filtering theory, is quick and easy to compute, generalisable, deterministic and unlike many current methods, requires no change-point or window size assumptions. We model R as a flexible, hidden Markov state process and exactly solve forward-backward algorithms, to derive R estimates that incorporate all available incidence information. This unifies and extends two popular methods, EpiEstim, which considers past incidence, and the Wallinga-Teunis method, which looks forward in time. We find that this combination of maximising information and minimising assumptions significantly reduces the bias and variance of R estimates. Moreover, these properties make EpiFilter more statistically robust in periods of low incidence, where several existing methods can become destabilised. As a result, EpiFilter offers improved inference of time-varying transmission patterns that are advantageous for assessing the risk of upcoming waves of infection or the influence of interventions, in real time and at various spatial scales.

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Economic Institutions and Growth Nexus: The Role of Governance and Democratic Institutions—Evidence from Time Varying Parameters’ (TVPs) Models

The Pakistan Development Review ◽

10.30541/v55i4i-iipp.675-688 ◽

2016 ◽

Vol 55 (4I-II) ◽

pp. 675-688

Author(s):

Ghulam Murtaza ◽

Muhammad Zahir Faridi

Keyword(s):

Structural Changes ◽

Jel Classification ◽

Economic Institutions ◽

Time Varying ◽

Democratic Institutions ◽

Main Hypothesis ◽

Dynamic Relationship ◽

Rolling Window

The present study has investigated the channels through which the linkage between economic institutions and growth is gauged, by addressing the main hypothesis of the study that whether quality of governance and democratic institutions set a stage for economic institutions to promote the long-term growth process in Pakistan. To test the hypothesis empirically, our study models the dynamic relationship between growth and economic institutions in a time varying framework in order to capture institutional developments and structural changes occurred in the economy of Pakistan over the years. Study articulates that, along with some customary specifics, the quality of government and democracy are the substantial factors that affect institutional quality and ultimately cause to promote growth in Pakistan. JEL Classification: O40; P16; C14; H10 Keywords: Economic Institutions, Growth, Governance and Democracy, Rolling Window Two-stage Least Squares, Pakistan

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Temporal dynamics of viral load and false negative rate influence the levels of testing necessary to combat COVID-19 spread

Scientific Reports ◽

10.1038/s41598-021-88498-9 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Katherine F. Jarvis ◽

Joshua B. Kelley

Keyword(s):

Viral Load ◽

Temporal Dynamics ◽

Reproduction Number ◽

False Negative ◽

False Negative Rate ◽

Agent Based Model ◽

Agent Based ◽

Viral Spread ◽

Negative Rate

AbstractColleges and other organizations are considering testing plans to return to operation as the COVID-19 pandemic continues. Pre-symptomatic spread and high false negative rates for testing may make it difficult to stop viral spread. Here, we develop a stochastic agent-based model of COVID-19 in a university sized population, considering the dynamics of both viral load and false negative rate of tests on the ability of testing to combat viral spread. Reported dynamics of SARS-CoV-2 can lead to an apparent false negative rate from ~ 17 to ~ 48%. Nonuniform distributions of viral load and false negative rate lead to higher requirements for frequency and fraction of population tested in order to bring the apparent Reproduction number (Rt) below 1. Thus, it is important to consider non-uniform dynamics of viral spread and false negative rate in order to model effective testing plans.

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PIN50 Leveraging Publicly Available Data to Estimate a Real-Time Reproduction Number (Rt) for Covid-19: A Comparison of Two Methods

Value in Health ◽

10.1016/j.jval.2021.04.1238 ◽

2021 ◽

Vol 24 ◽

pp. S114

Author(s):

S. Emerson ◽

K. Johnston ◽

A. Howarth ◽

J. Schneider ◽

M. Friesen ◽

...

Keyword(s):

Real Time ◽

Reproduction Number ◽

Time Reproduction

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Heterogeneity and effectiveness analysis of COVID-19 prevention and control in major cities in China through time-varying reproduction number estimation

Scientific Reports ◽

10.1038/s41598-020-79063-x ◽

2020 ◽

Vol 10 (1) ◽

Author(s):

Qing Cheng ◽

Zeyi Liu ◽

Guangquan Cheng ◽

Jincai Huang

Keyword(s):

Prevention And Control ◽

Large Scale ◽

Reproduction Number ◽

Correlation Method ◽

Control Measures ◽

Time Varying ◽

Short Period ◽

Significant Difference ◽

Prevention And Control Measures ◽

And Control

AbstractBeginning on December 31, 2019, the large-scale novel coronavirus disease 2019 (COVID-19) emerged in China. Tracking and analysing the heterogeneity and effectiveness of cities’ prevention and control of the COVID-19 epidemic is essential to design and adjust epidemic prevention and control measures. The number of newly confirmed cases in 25 of China’s most-affected cities for the COVID-19 epidemic from January 11 to February 10 was collected. The heterogeneity and effectiveness of these 25 cities’ prevention and control measures for COVID-19 were analysed by using an estimated time-varying reproduction number method and a serial correlation method. The results showed that the effective reproduction number (R) in 25 cities showed a downward trend overall, but there was a significant difference in the R change trends among cities, indicating that there was heterogeneity in the spread and control of COVID-19 in cities. Moreover, the COVID-19 control in 21 of 25 cities was effective, and the risk of infection decreased because their R had dropped below 1 by February 10, 2020. In contrast, the cities of Wuhan, Tianmen, Ezhou and Enshi still had difficulty effectively controlling the COVID-19 epidemic in a short period of time because their R was greater than 1.

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