scholarly journals Tracking R of COVID-19: A new real-time estimation using the Kalman filter

PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0244474 ◽  
Author(s):  
Francisco Arroyo-Marioli ◽  
Francisco Bullano ◽  
Simas Kucinskas ◽  
Carlos Rondón-Moreno
Keyword(s):  
Growth Rate ◽  
Kalman Filter ◽  
Reproduction Number ◽  
Time Estimation ◽  
Sir Model ◽  
Time Varying ◽  
The World ◽  
Real Time Estimation ◽  
Image Position ◽  
Pharmaceutical Interventions

We develop a new method for estimating the effective reproduction number of an infectious disease (R) and apply it to track the dynamics of COVID-19. The method is based on the fact that in the SIR model, R is linearly related to the growth rate of the number of infected individuals. This time-varying growth rate is estimated using the Kalman filter from data on new cases. The method is easy to implement in standard statistical software, and it performs well even when the number of infected individuals is imperfectly measured, or the infection does not follow the SIR model. Our estimates of R for COVID-19 for 124 countries across the world are provided in an interactive online dashboard, and they are used to assess the effectiveness of non-pharmaceutical interventions in a sample of 14 European countries.

scholarly journals Dynamics of Transmission and Control of COVID-19: A Real-time Estimation Using the Kalman Filter

2020 ◽  
Author(s):  
Francisco Arroyo Marioli ◽  
Francisco Bullano ◽  
Carlos Rondón-Moreno
Keyword(s):  
Kalman Filter ◽  
South Korea ◽  
Real Time ◽  
Reproduction Number ◽  
Time Estimation ◽  
Control Measures ◽  
Significant Heterogeneity ◽  
Real Time Estimation ◽  
And Control ◽  
Over Time

AbstractThe COVID-19 pandemic has become the center of attention for both researchers and authorities. In this paper, we propose and test a methodology to estimate the daily effective reproduction number (ℛt) through the lens of the Kalman Filter and Bayesian estimation. Moreover, we apply our method to data from the current COVID-19 pandemic in China, Italy, Japan, and South Korea. We correlate our findings with the implementation of control measures in each of these countries. Our results show that China, Italy, and South Korea have been able to reduce ℛt over time. We find significant heterogeneity in the way ℛt decreases across countries. For instance, China reduced ℛt from its peak to below one in 19 days, while South Korea achieved the same reduction in 12 days. In contrast, it has taken Italy almost a month to reach similar levels. We hypothesize this is related to how strict, enforceable, and comprehensive are the implemented policies.

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

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).

scholarly journals A Mobile Kalman-Filter Based Solution for the Real-Time Estimation of Spatio-Temporal_newline Gait Parameters

2016 ◽  
Vol 24 (7) ◽  
pp. 764-773 ◽  
Author(s):  
Alberto Ferrari ◽  
Pieter Ginis ◽  
Michael Hardegger ◽  
Filippo Casamassima ◽  
Laura Rocchi ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Real Time ◽  
Time Estimation ◽  
The Real ◽  
Gait Parameters ◽  
Real Time Estimation

scholarly journals Assessing the lockdown effect from excess mortalities

2021 ◽  
Author(s):  
Alexej Weber
Keyword(s):  
Growth Rate ◽  
South Korea ◽  
Growth Rates ◽  
Excess Mortality ◽  
Reproduction Number ◽  
Average Growth Rate ◽  
Average Growth ◽  
Reproduction Numbers ◽  
The Difference ◽  
Pharmaceutical Interventions

AbstractBackground and AimsThe reported case numbers of COVID-19 are often used to estimate the reproduction number or the growth rate. We use the excess mortality instead, showing the difference between most restrictive non-pharmaceutical interventions (mrNPIs) and less restrictive NPIs (lrNPIs) with respect to the growth rate and death counts.MethodsWe estimate the COVID-19 growth rate for Sweden, South Korea, Italy and Germany from the excess mortality. We use the average growth rate obtained for Sweden and South Korea, two countries with lrNPIs, to estimate additional death numbers in Germany and Italy (two countries with mrNPIs) in a hypothetic lrNPIs scenario.ResultsThe growth rate estimated from excess mortality decreased faster for Germany and Italy than for Sweden and South Korea, suggesting that the mrNPIs have a non-negligible effect. This is not visible when the growth rate is calculated using the reported case numbers of COVID-19. This results in approximately 4 500 and 12 000 more death numbers for Germany and Italy, respectively.ConclusionThe reproduction numbers or growth rates obtained from reported COVID-19 cases are most likely biased. Expanding testing capacity led to an overestimation of the growth rate across all countries analyzed, masking the true decrease already visible in the excess mortality. Using our method, a more realistic estimate of the growth rate is obtained. Conclusions made for the reproduction number derived from the reported case numbers like the insignificance of most restrictive non-pharmaceutical interventions (lockdowns) might be wrong and have to be reevaluated using the growth rates obtained with our method.

scholarly journals The risk for a new COVID-19 wave – and how it depends on R0, the current immunity level and current restrictions

2020 ◽  
Author(s):  
Tom Britton ◽  
Pieter Trapman ◽  
Frank Ball
Keyword(s):  
Preventive Measures ◽  
Reproduction Number ◽  
Social Activity ◽  
Herd Immunity ◽  
Time Varying ◽  
The World ◽  
Two Factors ◽  
Second Wave ◽  
Different Parts ◽  
Future Outbreak

AbstractThe COVID-19 pandemic has hit different parts of the world differently: some regions are still in the rise of the first wave, other regions are now facing a decline after a first wave, and yet other regions have started to see a second wave. The current immunity level î in a region is closely related to the cumulative fraction infected, which primarily depends on two factors: a) the initial potential for COVID-19 in the region (often quantified by the basic reproduction number R0), and b) the timing, amount and effectiveness of preventive measures put in place. By means of a mathematical model including heterogeneities owing to age, social activity and susceptibility, and allowing for time-varying preventive measures, the risk for a new epidemic wave and its doubling time, and how they depend on R0, î and the overall effect of the current preventive measures, are investigated. Focus lies on quantifying the minimal overall effect of preventive measures pMin needed to prevent a future outbreak. The first result shows that the current immunity level î plays a more influential roll than when immunity is obtained from vaccination. Secondly, by comparing regions with different R0 and î it is shown that regions with lower R0 and low î may now need higher preventive measures (pMin) compared with other regions having higher R0 but also higher î, even when such immunity levels are far from herd immunity.

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