Computing the daily reproduction number of COVID-19 by inverting the renewal equation using a variational technique

The COVID-19 pandemic has undergone frequent and rapid changes in its local and global infection rates, driven by governmental measures or the emergence of new viral variants. The reproduction number Rt indicates the average number of cases generated by an infected person at time t and is a key indicator of the spread of an epidemic. A timely estimation of Rt is a crucial tool to enable governmental organizations to adapt quickly to these changes and assess the consequences of their policies. The EpiEstim method is the most widely accepted method for estimating Rt. But it estimates Rt with a significant temporal delay. Here, we propose a method, EpiInvert, that shows good agreement with EpiEstim, but that provides estimates of Rt several days in advance. We show that Rt can be estimated by inverting the renewal equation linking Rt with the observed incidence curve of new cases, it. Our signal-processing approach to this problem yields both Rt and a restored it corrected for the “weekend effect” by applying a deconvolution and denoising procedure. The implementations of the EpiInvert and EpiEstim methods are fully open source and can be run in real time on every country in the world and every US state.

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Explaining the Effective Reproduction Number of COVID-19 through Mobility and Enterprise Statistics: Evidence from the First Wave in Japan

10.1101/2020.10.08.20209643 ◽

2020 ◽

Author(s):

Yoshio Kajitani ◽

Michinori Hatayama

Keyword(s):

Hospitality Industry ◽

Census Data ◽

Reproduction Number ◽

Data Sets ◽

Infected Person ◽

Infection Rates ◽

Location Data ◽

Data Source ◽

General Business

AbstractThis study uses mobility statistics combined with business census data for the eight Japanese prefectures with the highest COVID-19 infection rates to study the effect of mobility reductions on the effective reproduction number (i.e., the average number of secondary cases caused by one infected person). Mobility statistics are a relatively new data source created by compiling smartphone location data. Based on data for the first wave of infections in Japan, we found that reductions targeting the hospitality industry were more effective than restrictions on general business activities. Specifically, we found that to hold back the pandemic (that is, to reduce the effective reproduction number to one or less for all days), a 20-35% reduction in weekly mobility is required, depending on the region. A lesser goal, 80% of days with one or less observed transmission, can be achieved with a 6-30% reduction in weekly mobility. These are the results if other potential causes of spread are ignored; more careful observations and expanded data sets are needed.

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Explaining the effective reproduction number of COVID-19 through mobility and enterprise statistics: Evidence from the first wave in Japan

PLoS ONE ◽

10.1371/journal.pone.0247186 ◽

2021 ◽

Vol 16 (3) ◽

pp. e0247186

Author(s):

Yoshio Kajitani ◽

Michinori Hatayama

Keyword(s):

Hospitality Industry ◽

Census Data ◽

Reproduction Number ◽

Data Sets ◽

Infected Person ◽

Economic Data ◽

Infection Rates ◽

Location Data ◽

Data Source ◽

General Business

This study uses mobility statistics combined with business census data for the eight Japanese prefectures with the highest coronavirus disease-2019 (COVID-19) infection rates to study the effect of mobility reductions on the effective reproduction number (i.e., the average number of secondary cases caused by one infected person). Mobility statistics are a relatively new data source created by compiling smartphone location data; they can be effectively used for understanding pandemics if integrated with epidemiological findings and other economic data sets. Based on data for the first wave of infections in Japan, we found that reductions targeting the hospitality industry were slightly more effective than restrictions on general business activities. Specifically, we found that to hold back the pandemic (that is, to reduce the effective reproduction number to one or less for all days), a 20%–35% reduction in weekly mobility is required, depending on the region. A lesser goal, 80% of days with one or less observed transmission, can be achieved with a 6%–30% reduction in weekly mobility. These are the results if other potential causes of spread are ignored; for a fuller picture, more careful observations, expanded data sets, and advanced statistical modeling are needed.

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EPIDEMIC SPREADING ON THREE-LAYER INTERDEPENDENT NETWORKS

Journal of Biological System ◽

10.1142/s0218339016500248 ◽

2016 ◽

Vol 24 (04) ◽

pp. 469-494 ◽

Cited By ~ 2

Author(s):

LINGNA WANG ◽

GUANGHU ZHU ◽

HUIYAN KANG ◽

XINCHU FU

Keyword(s):

Infection Rate ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Mean Field ◽

Network Size ◽

Infection Rates ◽

Epidemic Spreading ◽

Interdependent Networks ◽

Coupled Networks ◽

The Basic Reproduction Number

Many epidemic diseases spread among three different populations with different contact patterns and infection rates. In response to such diseases, we propose two new types of three-layer interdependent networks — string-coupled networks and circular-coupled networks. We investigate an epidemic spreading on the two types of interdependent networks, propose two mathematical models through heterogeneous mean field approach and prove global stability of the disease-free and endemic equilibria. Through theoretical and numerical analysis, we find the following: the increase of each infection rate affects effectively only its own subnetwork and neighbors; in a string-coupled network, the middle subnetwork has bigger impact on the basic reproduction number than the end subnetworks with the growth of network size or infection rates; the basic reproduction number on a circular-coupled network is larger than that on a string-coupled network for a fixed network size; but the change of the basic reproduction number (or the average infection densities) is almost the same on both string-coupled and circular-coupled networks with the increasing of certain infection rate.

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The mathematics of the reproduction number R for Covid-19: A primer for demographers

10.1553/populationyearbook2022.res1.3 ◽

2021 ◽

Author(s):

Luis Rosero-Bixby ◽

Tim Miller

Keyword(s):

Infection Control ◽

Time Constant ◽

Reproduction Number ◽

Control Strategies ◽

Weighted Average ◽

Reproduction Rate ◽

Economic Costs ◽

Key Indicator ◽

Net Reproduction ◽

Over Time

The reproduction number R is a key indicator used to monitor the dynamics of Covid-19 and to assess the effects of infection control strategies that frequently have high social and economic costs. Despite having an analog in demography’s “net reproduction rate” that has been routinely computed for a century, demographers may not be familiar with the concept and measurement of R in the context of Covid-19. This article is intended to be a primer for understanding and estimating R in demography. We show that R can be estimated as a ratio between the numbers of new cases today divided by the weighted average of cases in previous days. We present two alternative derivations for these weights based on how risks have changed over time: constant vs. exponential decay. We then provide estimates of these weights, and demonstrate their use in calculating R to trace the course of the first pandemic year in 53 countries.

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Relationship between temperature and apparent shape of pristine ice crystals derived from polarimetric cloud radar observations during the ACCEPT campaign

Atmospheric Measurement Techniques ◽

10.5194/amt-9-3739-2016 ◽

2016 ◽

Vol 9 (8) ◽

pp. 3739-3754 ◽

Cited By ~ 19

Author(s):

Alexander Myagkov ◽

Patric Seifert ◽

Ulla Wandinger ◽

Johannes Bühl ◽

Ronny Engelmann

Keyword(s):

Free Fall ◽

Crystal Shape ◽

Ice Crystal ◽

Ambient Conditions ◽

Axis Ratio ◽

Microwave Scattering ◽

Cloud Radar ◽

Ice Particles ◽

Rapid Changes ◽

Good Agreement

Abstract. This paper presents first quantitative estimations of apparent ice particle shape at the top of liquid-topped clouds. Analyzed ice particles were formed under mixed-phase conditions in the presence of supercooled water and in the temperature range from −20 to −3 °C. The estimation is based on polarizability ratios of ice particles measured by a Ka-band cloud radar MIRA-35 with hybrid polarimetric configuration. Polarizability ratio is a function of the geometrical axis ratio and the dielectric properties of the observed hydrometeors. For this study, 22 cases observed during the ACCEPT (Analysis of the Composition of Clouds with Extended Polarization Techniques) field campaign were used. Polarizability ratios retrieved for cloud layers with the cloud-top temperatures of ∼ −5, ∼ −8, ∼ −15, and ∼ −20 °C were 1.6, 0.9, 0.6, and 0.9, respectively. Such values correspond to prolate, quasi-isotropic, oblate, and quasi-isotropic particles, respectively. Data from a free-fall chamber were used for the comparison. A good agreement of detected apparent shapes with well-known shape–temperature dependencies observed in laboratories was found. Polarizability ratios used for the analysis were estimated for areas located close to the cloud top, where aggregation and riming processes do not strongly affect ice particles. We concluded that, in microwave scattering models, ice particles detected in these areas can be assumed to have pristine shapes. It was also found that even slight variations of ambient conditions at the cloud top with temperatures warmer than ∼ −5 °C can lead to rapid changes of ice crystal shape.

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A method for monitoring hydrological conditions beneath herbaceous wetlands using multi-temporal ALOS PALSAR coherence data

ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences ◽

10.5194/isprsarchives-xl-7-w4-221-2015 ◽

2015 ◽

Vol XL-7/W4 ◽

pp. 221-226 ◽

Cited By ~ 2

Author(s):

M. Zhang ◽

Z. Li ◽

B. Tian ◽

J. Zhou ◽

J. Zeng

Keyword(s):

Effective Area ◽

Interferometric Synthetic Aperture Radar ◽

Alos Palsar ◽

Hydrological Conditions ◽

In Situ Data ◽

Key Indicator ◽

Multi Temporal ◽

First Time ◽

Good Agreement

Reed marshes, the world’s most widespread type of wetland vegetation, are undergoing major changes as a result of climate changes and human activities. The presence or absence of water in reed marshes has a significant impact on the whole ecosystem and remains a key indicator to identify the effective area of a wetland and help estimate the degree of degeneration. Past studies have demonstrated the use of interferometric synthetic aperture radar (InSAR) to map water-level changes for flooded reeds. However, the identification of the different hydrological states of reed marshes is often poorly understood. The analysis given in this paper shows that L-band interferometric coherence is very sensitive to the water surface conditions beneath reed marshes and so can be used as classifier. A method based on a statistical analysis of the coherence distributions for wet and dry reeds using InSAR pairs was, therefore, investigated in this study. The experimental results were validated by in-situ data and showed very good agreement. This is the first time that information about the water cover under herbaceous wetlands has been derived using interferometric coherence values. This method can also effectively and easily be applied to monitor the hydrological conditions beneath other herbaceous wetlands.

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Epidemic Big Bang: development and quarantine measures for Covid-19

10.21203/rs.3.rs-37836/v1 ◽

2020 ◽

Author(s):

Sergey Trigger ◽

Eugeny Czerniawski

Keyword(s):

Statistical Data ◽

Reproduction Number ◽

Big Bang ◽

Infected Person ◽

Good Correspondence ◽

Closed Population ◽

Infinite Population ◽

Duration Of Disease ◽

The Mean ◽

Day By Day

Abstract New discrete approximation for the infection spread is constructed based on COVID-19 epidemic data. We consider the epidemic as dependent upon four key parameters: the size of population involved, the mean number of dangerous contacts of one infected person per day, the probability to transmit infection due to such contact and the mean duration of disease. In the simplest case of free epidemic in an infinite population, the number of infected rises exponentially day by day. Here we show the model for epidemic process in a closed population, constrained by isolation, treatment and so on. The four parameters introduced here have the clear sense and are in association with the well-known concept of reproduction number in the continuous susceptible-infected-susceptible model. We derive these parameters from the adequate statistical data. On this basis, we also found the corresponding basic reproduction number mentioned above. Our approach allows evaluating the influence of quarantine measures on free pandemic process. We found a good correspondence of the theory and reliable statistical data. The model is quite flexible and it can be expanded for situations that are more complex.

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Data driven inference of the reproduction number (R0) for COVID-19 before and after interventions for 51 European countries

10.1101/2020.05.21.20109314 ◽

2020 ◽

Cited By ~ 2

Author(s):

Petr Karnakov ◽

Georgios Arampatzis ◽

Ivica Kičić ◽

Fabian Wermelinger ◽

Daniel Wälchli ◽

...

Keyword(s):

Reproduction Number ◽

European Countries ◽

Data Driven ◽

Geographic Proximity ◽

Online Tool ◽

Key Indicator ◽

Efficient Sampling ◽

Before And After ◽

Sampling Algorithms ◽

Bayesian Inference Framework

The reproduction number (R0) is broadly considered as a key indicator for the spreading of the COVID-19 pandemic. The estimation of its value with respect to the key threshold of 1.0 is a measure of the need, and eventually effectiveness, of interventions imposed in various countries. Here we present an online tool for the data driven inference and quantification of uncertainties for R0 as well as the time points of interventions for 51 European countries. The study relies on the Bayesian calibration of the simple and well established SIR model with data from reported daily infections. The model is able to fit the data for most countries without individual tuning of parameters. We deploy an open source Bayesian inference framework and efficient sampling algorithms to present a publicly available GUI (https://www.cse-lab.ethz.ch/coronavirus/) that allows the user to assess custom data and compare predictions for pairs of European countries. The results provide a ranking based on the rate of the disease's spread suggesting a metric for the effectiveness of social distancing measures. They also serve to demonstrate how geographic proximity and related times of interventions can lead to similarities in the progression of the epidemic.

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Microsimulation of SARS-CoV-2 Transmission in Society

10.1101/2021.05.16.21257298 ◽

2021 ◽

Author(s):

Anthony R Green ◽

Daniel Keep ◽

Ian Piper

Keyword(s):

Basic Reproductive Number ◽

Reproductive Number ◽

Infection Model ◽

Infection Rates ◽

Social Distancing ◽

Source Of Infection ◽

Population Sizes ◽

Doubling Times ◽

Good Agreement ◽

Infection Spread

The outbreak of the pandemic disease, COVID-19, has shown that the approaches by different countries has resulted in a range of infection rates through their societies. This has arisen from the varying personal behaviour and tactical use of lockdown strategies within each country. We report the use of microsimulation of a simulated community in Australia, using a discrete infection model within a community of residences, places of work and recreation to demonstrate the applicability of this method to both the current pandemic and to infection more generally. Simulations without any societal intervention on infection spread provided base simulations that could be compared with social and societal controls in the future and which were compared with the initial doubling times of country outbreaks across the world. Different population sizes were represented in some simulations and in other simulations the effects of either social distancing or the use of facial masks as personal behaviours was investigated within the community. Good agreement is found between the initial doubling times for several countries and the simulations that suggests that modelling infection as a collection of individual infections provides an alternative to current epidemiological models. The variation of the basic reproductive number, R0, with time and population size, suggests that one of the fundamentals assumptions in SIR type models is wrong, but varies according to the properties of the population being modelled. Investigation of the infection spread shows that the number of super-spreaders varies with the size of the population and occurs through contacts in clubs, supermarkets, schools and theatres where the source of infection is an employee and where there are high numbers of contacts. The simulations of individual control show that the benefits of social distancing or wearing masks is only fully realised where there is considerable compliance within society to these measures.

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The SIR model towards the Data One year of Covid-19 pandemic in Italy case study and plausible "real" numbers.

10.21203/rs.3.rs-605751/v1 ◽

2021 ◽

Author(s):

Ignazio Lazzizzera

Keyword(s):

Generation Time ◽

Reproduction Number ◽

Removal Rate ◽

Infectious Period ◽

Third Wave ◽

Real Numbers ◽

Study Case ◽

One Year ◽

Good Agreement

Abstract In this work, the SIR epidemiological model is reformulated so to highlight the important effective reproduction number, as well as to account for the generation time, the inverse of the incidence rate, and the infectious period (or removal period), the inverse of the removal rate. The aim is to check whether the relationships the model poses among the various observables are actually found in the data. The study case of the second through the third wave of the Covid-19 pandemic in Italy is taken. Given its scale invariance, initially the model is tested with reference to the curve of swab-confirmed infectious individuals only. It is found to match the data if the curve of the removed (that is healed or deceased) individuals is assumed underestimated by a factor of about 3 together with other related curves. Contextually, the generation time and the removal period, as well as the effective reproduction number, are obtained fitting the SIR equations to the data; the outcomes prove to be in good agreement with those of other works. Then, using knowledge of the proportion of Covid-19 transmissions likely occurring from individuals who didn't develop symptoms, thus mainly undetected, an estimate of the "real numbers'' of the epidemic is obtained, looking also in good agreement with results from other, completely different works. The line of this work is new and the procedures, computationally really inexpensive, can be applied to any other national or regional case besides Italy's study case here.

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