scholarly journals A Convex Optimization Solution for the Effective Reproduction NumberRt

2021 ◽  
Author(s):  
Joaquín Salas
Keyword(s):  
Infectious Disease ◽  
Linear System ◽  
Convex Optimization ◽  
Reproduction Number ◽  
Renewal Equation ◽  
Birth Process ◽  
Transmission Rates ◽  
Slowing Down

AbstractCOVID-19 is a global infectious disease that has affected millions of people. With new variants emerging with augmented transmission rates, slowing down of vaccine rollouts, and rising new cases threatening sanitary capabilities to the brink of collapse, there is the need to continue studying more effective forms to track its spread. This paper presents a strategy to compute the effective reproduction numberRt. Our method starts with a form of the renewal equation of the birth process specially suitable to computeRt. After showing that one can express it as a linear system, we proceed to solve it, along with appropriate constraints, using convex optimization. We demonstrate the method’s effectiveness using synthetic and real sequences of infections and comparing it with a leading approach.

scholarly journals Inferring R 0 in emerging epidemics—the effect of common population structure is small

2016 ◽  
Vol 13 (121) ◽  
pp. 20160288 ◽  
Author(s):  
Pieter Trapman ◽  
Frank Ball ◽  
Jean-Stéphane Dhersin ◽  
Viet Chi Tran ◽  
Jacco Wallinga ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Population Structure ◽  
Robust Control ◽  
Reproduction Number ◽  
Contact Structures ◽  
Emerging Infections ◽  
Control Effort ◽  
Large Outbreak ◽  
Epidemiological Parameters ◽  
The Basic Reproduction Number

When controlling an emerging outbreak of an infectious disease, it is essential to know the key epidemiological parameters, such as the basic reproduction number R 0 and the control effort required to prevent a large outbreak. These parameters are estimated from the observed incidence of new cases and information about the infectious contact structures of the population in which the disease spreads. However, the relevant infectious contact structures for new, emerging infections are often unknown or hard to obtain. Here, we show that, for many common true underlying heterogeneous contact structures, the simplification to neglect such structures and instead assume that all contacts are made homogeneously in the whole population results in conservative estimates for R 0 and the required control effort. This means that robust control policies can be planned during the early stages of an outbreak, using such conservative estimates of the required control effort.

scholarly journals SARS-CoV-2 lineage dynamics in England from September to November 2021: high diversity of Delta sub-lineages and increased transmissibility of AY.4.2

2021 ◽  
Author(s):  
Oliver Eales ◽  
Andrew Page ◽  
Leonardo de Oliveira Martins ◽  
Haowei Wang ◽  
Barbara Bodinier ◽  
...  
Keyword(s):  
Mutation Rate ◽  
Immune Escape ◽  
Evolutionary Rate ◽  
Reproduction Number ◽  
Natural Infection ◽  
Community Sample ◽  
Rt Pcr ◽  
Slowing Down ◽  
Routine Surveillance ◽  
Community Transmission

Since the emergence of SARS-CoV-2, evolutionary pressure has driven large increases in the transmissibility of the virus. However, with increasing levels of immunity through vaccination and natural infection the evolutionary pressure will switch towards immune escape. Here we present phylogenetic relationships and lineage dynamics within England (a country with high levels of immunity), as inferred from a random community sample of individuals who provided a self-administered throat and nose swab for rt-PCR testing as part of the REal-time Assessment of Community Transmission-1 (REACT-1) study. From 9 to 27 September 2021 (round 14) and 19 October to 5 November 2021 (round 15), all lineages sequenced within REACT-1 were Delta or a Delta sub-lineage with 44 unique lineages identified. The proportion of the original Delta variant (B.1.617.2) was found to be increasing between September and November 2021, which may reflect an increasing number of sub-lineages which have yet to be identified. The proportion of B.1.617.2 was greatest in London, which was further identified as a region with an increased level of genetic diversity. The Delta sub-lineage AY.4.2 was found to be robustly increasing in proportion, with a reproduction number 15% (8%, 23%) greater than its parent and most prevalent lineage, AY.4. Both AY.4.2 and AY.4 were found to be geographically clustered in September but this was no longer the case by late October/early November, with only the lineage AY.6 exhibiting clustering towards the South of England. Though no difference in the viral load based on cycle threshold (Ct) values was identified, a lower proportion of those infected with AY.4.2 had symptoms for which testing is usually recommend (loss or change of sense of taste, loss or change of sense of smell, new persistent cough, fever), compared to AY.4 (p = 0.026). The evolutionary rate of SARS-CoV-2, as measured by the mutation rate, was found to be slowing down during the study period, with AY.4.2 further found to have a reduced mutation rate relative to AY.4. As SARS-CoV-2 moves towards endemicity and new variants emerge, genomic data obtained from random community samples can augment routine surveillance data without the potential biases introduced due to higher sampling rates of symptomatic individuals.

The basic reproduction number

2012 ◽  
Author(s):  
Odo Diekmann ◽  
Hans Heesterbeek ◽  
Tom Britton
Keyword(s):  
Infectious Disease ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Infected Individual ◽  
Vital Role ◽  
Point Of View ◽  
Epidemiological Models ◽  
Disease Epidemiology ◽  
Infectious Disease Epidemiology ◽  
The Basic Reproduction Number

The basic reproduction number (or ratio) R₀ is arguably the most important quantity in infectious disease epidemiology. It is among the quantities most urgently estimated for infectious diseases in outbreak situations, and its value provides insight when designing control interventions for established infections. From a theoretical point of view R₀ plays a vital role in the analysis of, and consequent insight from, infectious disease models. There is hardly a paper on dynamic epidemiological models in the literature where R₀ does not play a role. R₀ is defined as the average number of new cases of an infection caused by one typical infected individual, in a population consisting of susceptibles only. This chapter shows how R₀ can be characterized mathematically and provides detailed examples of its calculation in terms of parameters of epidemiological models, culminating in a set of algorithms (or “recipes”) for the calculation for compartmental epidemic systems.

scholarly journals Time Course of COVID-19 Cases in Austria

2020 ◽  
Vol 17 (9) ◽  
pp. 3270 ◽  
Author(s):  
Hanns Moshammer ◽  
Michael Poteser ◽  
Kathrin Lemmerer ◽  
Peter Wallner ◽  
Hans-Peter Hutter
Keyword(s):  
Public Health ◽  
Infectious Disease ◽  
Time Course ◽  
Reproduction Number ◽  
Average Duration ◽  
Northern Italy ◽  
Reproduction Rate ◽  
Health Measures ◽  
Major Outbreak ◽  
Novel Coronavirus

COVID-19 is an infectious disease caused by a novel coronavirus, which first appeared in China in late 2019, and reached pandemic distribution in early 2020. The first major outbreak in Europe occurred in Northern Italy where it spread to neighboring countries, notably to Austria, where skiing resorts served as a main transmission hub. Soon, the Austrian government introduced strict measures to curb the spread of the virus. Using publicly available data, we assessed the efficiency of the governmental measures. We assumed an average incubation period of one week and an average duration of infectivity of 10 days. One week after the introduction of strict measures, the increase in daily new cases was reversed, and the reproduction number dropped. The crude estimates tended to overestimate the reproduction rate in the early phase. Publicly available data provide a first estimate about the effectiveness of public health measures. However, more data are needed for an unbiased assessment.

scholarly journals Definition and estimation of an actual reproduction number describing past infectious disease transmission: application to HIV epidemics among homosexual men in Denmark, Norway and Sweden

2004 ◽  
Vol 132 (6) ◽  
pp. 1139-1149 ◽  
Author(s):  
E. J. AMUNDSEN ◽  
H. STIGUM ◽  
J.-A. RØTTINGEN ◽  
O. O. AALEN
Keyword(s):  
Infectious Disease ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Infectious Period ◽  
Secondary Case ◽  
Time Interval ◽  
Homosexual Men ◽  
Infectious Disease Transmission ◽  
A Value ◽  
The Common

Prevalence and incidence measures are the common way to describe epidemics. The reproduction number supplies information on the potential for growth or decline of an epidemic. We define an actual reproduction number for infectious disease transmission that has taken place. An estimator is suggested, based on the number of new infections observed in a given time-interval, the number of those infected at the start of the interval, and the length of the infectious period. That estimator is applied to HIV among men having sex with other men over the period, 1977–1995, in Scandinavia. The actual reproduction number was estimated with acceptable certainty from the period, 1981–1982, yielding a value of 15 secondary cases. A value of less than one secondary case was assessed for the period, 1988–1995, in Denmark and Sweden. The actual reproduction number gives us some additional understanding of the dynamics of epidemics, compared with prevalence and incidence curves.

scholarly journals Threshold parameters for a model of epidemic spread among households and workplaces

2009 ◽  
Vol 6 (40) ◽  
pp. 979-987 ◽  
Author(s):  
L. Pellis ◽  
N. M. Ferguson ◽  
C. Fraser
Keyword(s):  
Infectious Disease ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Model Parameters ◽  
Epidemic Spread ◽  
Threshold Parameter ◽  
Disease Epidemiology ◽  
Infectious Disease Epidemiology ◽  
Complex Models ◽  
The Basic Reproduction Number

The basic reproduction number R 0 is one of the most important concepts in modern infectious disease epidemiology. However, for more realistic and more complex models than those assuming homogeneous mixing in the population, other threshold quantities can be defined that are sometimes more useful and easily derived in terms of model parameters. In this paper, we present a model for the spread of a permanently immunizing infection in a population socially structured into households and workplaces/schools, and we propose and discuss a new household-to-household reproduction number R H for it. We show how R H overcomes some of the limitations of a previously proposed threshold parameter, and we highlight its relationship with the effort required to control an epidemic when interventions are targeted at randomly selected households.

scholarly journals Modelling suggests limited change in the reproduction number from reopening Norwegian kindergartens and schools during the COVID-19 pandemic

PLoS ONE ◽  
2021 ◽  
Vol 16 (2) ◽  
pp. e0238268
Author(s):  
Martin Rypdal ◽  
Veronika Rypdal ◽  
Per Kristen Jakobsen ◽  
Elinor Ytterstad ◽  
Ola Løvsletten ◽  
...  
Keyword(s):  
Reproduction Number ◽  
After School ◽  
School Closures ◽  
Considerable Uncertainty ◽  
Transmission Rates ◽  
Influenza Pandemics ◽  
Two Cities ◽  
Secondary Objective ◽  
Nonpharmaceutical Interventions

Background To suppress the COVID-19 outbreak, the Norwegian government closed all schools on March 13, 2020. The kindergartens reopened on April 20, and the schools on April 27 and May 11 of 2020. The effect of these measures is largely unknown since the role of children in the spread of the SARS-CoV-2 virus is still unclear. There are only a few studies of school closures as a separate intervention to other social distancing measures, and little research exists on the effect of school opening during a pandemic. Objective This study aimed to model the effect of opening kindergartens and the schools in Norway in terms of a change in the reproduction number (R). A secondary objective was to assess if we can use the estimated R after school openings to infer the rates of transmission between children in schools. Methods We used an individual-based model (IBM) to assess the reopening of kindergartens and schools in two Norwegian cities, Oslo, the Norwegian capital, with a population of approximately 680 000, and Tromsø, which is the largest city in Northern Norway, with a population of approximately 75 000. The model uses demographic information and detailed data about the schools in both cities. We carried out an ensemble study to obtain robust results in spite of the considerable uncertainty that remains about the transmission of SARS-CoV-2. Results We found that reopening of Norwegian kindergartens and schools are associated with a change in R of 0.10 (95%CI 0.04–0.16) and 0.14 (95%CI 0.01–0.25) in the two cities under investigation if the in-school transmission rates for the SARS-CoV-2 virus are equal to what has previously been estimated for influenza pandemics. Conclusion We found only a limited effect of reopening schools on the reproduction number, and we expect the same to hold true in other countries where nonpharmaceutical interventions have suppressed the pandemic. Consequently, current R-estimates are insufficiently accurate for determining the transmission rates in schools. For countries that have closed schools, planned interventions, such as the opening of selected schools, can be useful to infer general knowledge about children-to-children transmission of SARS-CoV-2.

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

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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