The association of community mobility with the time-varying reproduction number (R) of SARS-CoV-2: a modelling study across 330 local UK authorities

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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Development of the reproduction number from coronavirus SARS-CoV-2 case data in Germany and implications for political measures

BMC Medicine ◽

10.1186/s12916-020-01884-4 ◽

2021 ◽

Vol 19 (1) ◽

Author(s):

Sahamoddin Khailaie ◽

Tanmay Mitra ◽

Arnab Bandyopadhyay ◽

Marta Schips ◽

Pietro Mascheroni ◽

...

Keyword(s):

Structural Changes ◽

Reproduction Number ◽

National Level ◽

Transmission Dynamics ◽

Federal State ◽

Parameter Estimates ◽

Time Varying ◽

Short Term ◽

Robert Koch Institute ◽

Federal States

Abstract Background SARS-CoV-2 has induced a worldwide pandemic and subsequent non-pharmaceutical interventions (NPIs) to control the spread of the virus. As in many countries, the SARS-CoV-2 pandemic in Germany has led to a consecutive roll-out of different NPIs. As these NPIs have (largely unknown) adverse effects, targeting them precisely and monitoring their effectiveness are essential. We developed a compartmental infection dynamics model with specific features of SARS-CoV-2 that allows daily estimation of a time-varying reproduction number and published this information openly since the beginning of April 2020. Here, we present the transmission dynamics in Germany over time to understand the effect of NPIs and allow adaptive forecasts of the epidemic progression. Methods We used a data-driven estimation of the evolution of the reproduction number for viral spreading in Germany as well as in all its federal states using our model. Using parameter estimates from literature and, alternatively, with parameters derived from a fit to the initial phase of COVID-19 spread in different regions of Italy, the model was optimized to fit data from the Robert Koch Institute. Results The time-varying reproduction number (Rt) in Germany decreased to <1 in early April 2020, 2–3 weeks after the implementation of NPIs. Partial release of NPIs both nationally and on federal state level correlated with moderate increases in Rt until August 2020. Implications of state-specific Rt on other states and on national level are characterized. Retrospective evaluation of the model shows excellent agreement with the data and usage of inpatient facilities well within the healthcare limit. While short-term predictions may work for a few weeks, long-term projections are complicated by unpredictable structural changes. Conclusions The estimated fraction of immunized population by August 2020 warns of a renewed outbreak upon release of measures. A low detection rate prolongs the delay reaching a low case incidence number upon release, showing the importance of an effective testing-quarantine strategy. We show that real-time monitoring of transmission dynamics is important to evaluate the extent of the outbreak, short-term projections for the burden on the healthcare system, and their response to policy changes.

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COVID-19 epidemic monitoring after non-pharmaceutical interventions: The use of time-varying reproduction number in a country with a large migrant population

International Journal of Infectious Diseases ◽

10.1016/j.ijid.2020.08.039 ◽

2020 ◽

Vol 99 ◽

pp. 466-472 ◽

Cited By ~ 2

Author(s):

Adil Al Wahaibi ◽

Abdullah Al Manji ◽

Amal Al Maani ◽

Bader Al Rawahi ◽

Khalid Al Harthy ◽

...

Keyword(s):

Reproduction Number ◽

Time Varying ◽

Migrant Population ◽

Use Of Time ◽

Epidemic Monitoring ◽

Pharmaceutical Interventions

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Behavioral changes before lockdown, and decreased retail and recreation mobility during lockdown, contributed most to the successful control of the COVID-19 epidemic in 35 Western countries

10.1101/2020.06.20.20136382 ◽

2020 ◽

Cited By ~ 1

Author(s):

Koen Deforche ◽

Jurgen Vercauteren ◽

Viktor Müller ◽

Anne-Mieke Vandamme

Keyword(s):

Basic Reproduction Number ◽

Reproduction Number ◽

Independent Predictor ◽

Behavioral Changes ◽

Time Varying ◽

Anecdotal Evidence ◽

Tight Control ◽

Western Countries ◽

Successful Control ◽

Second Peak

The COVID-19 pandemic has prompted a lockdown in many countries to control the exponential spread of the SARS-CoV-2 virus (1, 2). This resulted in curbing the epidemic by reducing the time-varying basic reproduction number (Rt) to below one (3, 4). Governments are looking for evidence to balance the demand of their citizens to ease some of the restriction, against the fear of a second peak in infections. More details on the specific circumstances that promote exponential spread (i.e. Rt> 1) and the measures that contributed most to a reduction in Rt are needed. Here we show that in 33 of 35 Western countries (32 European, plus Israel, USA and Canada), Rt fell to around or below one during lockdown (March – May 2020). One third of the effect happened already on average 6 days before the lockdown, with lockdown itself causing another major drop in transmission. Country-wide compulsory usage of masks was implemented only in Slovakia 10 days into lockdown, and on its own reduced transmission by half. During lockdown, decreased mobility in retail and recreation was an independent predictor of lower Rt during lockdown, while changes in other types of mobility were not. These results are consistent with anecdotal evidence that large recreational gatherings are super-spreading events (5, 6), and may even suggest that infections during day-to-day contact at work are not sufficient to spark exponential growth. Our data suggest measures that will contribute to avoiding a second peak include a tight control on circumstances that facilitate massive spread such as large gatherings especially indoors, physical distancing, and mask use.

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COVID-19 Time-varying Reproduction Numbers Worldwide: An Empirical Analysis of Mandatory and Voluntary Social Distancing

10.1101/2021.04.06.21255033 ◽

2021 ◽

Author(s):

Alexander Chudik ◽

M. Hashem Pesaran ◽

Alessandro Rebucci

Keyword(s):

Reproduction Number ◽

Transmission Rate ◽

Economic Incentives ◽

Moment Condition ◽

Time Varying ◽

Linear Interaction ◽

Susceptible Population ◽

Social Distancing ◽

Transmission Rates ◽

Reproduction Numbers

AbstractThis paper estimates time-varying COVID-19 reproduction numbers worldwide solely based on the number of reported infected cases, allowing for under-reporting. Estimation is based on a moment condition that can be derived from an agent-based stochastic network model of COVID-19 transmission. The outcomes in terms of the reproduction number and the trajectory of per-capita cases through the end of 2020 are very diverse. The reproduction number depends on the transmission rate and the proportion of susceptible population, or the herd immunity effect. Changes in the transmission rate depend on changes in the behavior of the virus, re-flecting mutations and vaccinations, and changes in people’s behavior, reflecting voluntary or government mandated isolation. Over our sample period, neither mutation nor vaccination are major factors, so one can attribute variation in the transmission rate to variations in behavior. Evidence based on panel data models explaining transmission rates for nine European countries indicates that the diversity of outcomes resulted from the non-linear interaction of mandatory containment measures, voluntary precautionary isolation, and the economic incentives that gov-ernments provided to support isolation. These effects are precisely estimated and robust to various assumptions. As a result, countries with seemingly different social distancing policies achieved quite similar outcomes in terms of the reproduction number. These results imply that ignoring the voluntary component of social distancing could introduce an upward bias in the estimates of the effects of lock-downs and support policies on the transmission rates.JEL ClassificationD0, F6, C4, I120, E7

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

10.1101/2020.10.09.20209981 ◽

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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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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A Compartmental Epidemic Model Incorporating Probable Cases to Model COVID-19 Outbreak in Regions with Limited Testing Capacity

10.1101/2020.07.30.20165282 ◽

2020 ◽

Author(s):

Agus Hasan ◽

Yuki Nasution

Keyword(s):

Kalman Filter ◽

Extended Kalman Filter ◽

Epidemic Model ◽

Laboratory Testing ◽

Reproduction Number ◽

Well Posedness ◽

Time Varying ◽

Policy Makers ◽

Limited Testing ◽

The Basic Reproduction Number

We propose a new compartmental epidemic model taking into account people who has symptoms with no confirmatory laboratory testing (probable cases). We prove well-posedness of the model and provide an explicit expression for the basic reproduction number R0. We use the model together with an extended Kalman filter (EKF) to estimate the time-varying effective reproduction number Rt of COVID-19 in West Java province, Indonesia, where laboratory testing capacity is limited. Based on our estimation, the value of Rt is higher when the probable cases are taken into account. This correction can be used by decision and policy makers when considering re-opening policy and evaluation of measures.

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A new estimation method for COVID-19 time-varying reproduction number using active cases

10.1101/2020.06.28.20142158 ◽

2020 ◽

Cited By ~ 3

Author(s):

A. Hasan ◽

H. Susanto ◽

V.R. Tjahjono ◽

R. Kusdiantara ◽

E.R.M. Putri ◽

...

Keyword(s):

Reproduction Number ◽

Estimation Method ◽

Virus Transmission ◽

Estimation Procedure ◽

Time Varying ◽

State Variables ◽

Pass Filter ◽

Low Pass Filter ◽

Novel Coronavirus ◽

Stage Estimation

AbstractWe propose a new method to estimate the time-varying effective (or instantaneous) reproduction number of the novel coronavirus disease (COVID-19). The method is based on a discrete-time stochastic augmented compartmental model that describes the virus transmission. A two-stage estimation method, which combines the Extended Kalman Filter (EKF) to estimate reported state variables (active and removed cases) and a low pass filter based on a rational transfer function to remove short term fluctuations of the reported cases, is used with case uncertainties that are assumed to follow a Gaussian distribution. Our method does not require information regarding serial intervals, which makes the estimation procedure simpler without reducing the quality of the estimate. We show that the proposed method is comparable to common approaches, e.g., age-structured and new cases based sequential Bayesian models. We also apply it to COVID-19 cases in the Scandinavian countries: Denmark, Sweden, and Norway, where we see a delay of about four days in predicting the epidemic peak.

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