The front of the epidemic spread and first passage percolation

In this paper we establish a connection between epidemic models on random networks with general infection times considered in Barbour and Reinert 2013 and first passage percolation. Using techniques developed in Bhamidi, van der Hofstad, Hooghiemstra 2012, when each vertex has infinite contagious periods, we extend results on the epidemic curve in Barbour Reinert 2013 from bounded degree graphs to general sparse random graphs with degrees having finite third moments as the number of vertices tends to infinity. We also study the epidemic trail between the source and typical vertices in the graph. This connection to first passage percolation can be also be used to study epidemic models with general contagious periods as in Barbour Reinert 2013 without bounded degree assumptions.Comment: 14 page

Bayesian prediction of an epidemic curve

AbstractAn epidemic curve is a graph in which the number of new cases of an outbreak disease is plotted against time. Epidemic curves are ordinarily constructed after the disease outbreak is over. However, a good estimate of the epidemic curve early in an outbreak would be invaluable to health care officials. Currently, techniques for predicting the severity of an outbreak are very limited. As far as predicting the number of future cases, ordinarily epidemiologists simply make an educated guess as to how many people might become affected. We develop a model for estimating an epidemic curve early in an outbreak, and we show results of experiments testing its accuracy

Effectiveness of the measures to flatten the epidemic curve of COVID-19. The case of Spain

After the cases of COVID-19 skyrocketed, showing that it was no longer possible to contain the spread of the disease, the governments of many countries launched mitigation strategies, trying to slow the spread of the epidemic and flatten its curve. The Spanish Government adopted physical distancing measures on March 14; 13 days after the epidemic outbreak started its exponential growth. Our objective in this paper was to evaluate ex-ante (before the flattening of the curve) the effectiveness of the measures adopted by the Spanish Government to mitigate the COVID-19 epidemic. Our hypothesis was that the behavior of the epidemic curve is very similar in all countries. We employed a time series design, using information from January 17 to April 5, 2020 on the new daily COVID-19 cases from Spain, China and Italy. We specified two generalized linear mixed models (GLMM) with variable response from the Gaussian family (i.e. linear mixed models): one to explain the shape of the epidemic curve of accumulated cases and the other to estimate the effect of the intervention. Just one day after implementing the measures, the variation rate of accumulated cases decreased daily, on average, by 3.059 percentage points, (95% credibility interval: −5.371, −0.879). This reduction will be greater as time passes. The reduction in the variation rate of the accumulated cases, on the last day for which we have data, has reached 5.11 percentage points. The measures taken by the Spanish Government on March 14, 2020 to mitigate the epidemic curve of COVID-19 managed to flatten the curve and although they have not (yet) managed to enter the decrease phase, they are on the way to do so.Peer reviewe

A parsimonious description and cross-country analysis of COVID-19 epidemic curve

In a given country, the cumulative death toll of the first wave of the COVID-19 epidemic follows a sigmoid curve as a function of time. In most cases, the curve is well described by the Gompertz function, which is characterized by two essential parameters, the initial growth rate and the decay rate as the first epidemic wave subsides. These parameters are determined by socioeconomic factors and the countermeasures to halt the epidemic. The Gompertz model implies that the total death toll depends exponentially, and hence very sensitively, on the ratio between these rates. The remarkably different epidemic curves for the first epidemic wave in Sweden and Norway and many other countries are classified and discussed in this framework, and their usefulness for the planning of mitigation strategies is discussed.Comment: 27 pages, 14 figure

COVID-19 : nothing is normal in this pandemic

Funding: This work was partially support by CEAUL (funded by FCT – Fundação para a Ciência e a Tecnologia, Portugal, through the project UIDB/00006/2020).This manuscript brings attention to inaccurate epidemiological concepts that emerged during the COVID-19 pandemic. In social media and scientific journals, some wrong references were given to a "normal epidemic curve" and also to a "log-normal curve/distribution". For many years, textbooks and courses of reputable institutions and scientific journals have disseminated misleading concepts. For example, calling histogram to plots of epidemic curves or using epidemic data to introduce the concept of a Gaussian distribution, ignoring its temporal indexing. Although an epidemic curve may look like a Gaussian curve and be eventually modelled by a Gauss function, it is not a normal distribution or a log-normal, as some authors claim. A pandemic produces highly-complex data and to tackle it effectively statistical and mathematical modelling need to go beyond the "one-size-fits-all solution". Classical textbooks need to be updated since pandemics happen and epidemiology needs to provide reliable information to policy recommendations and actions.Publisher PDFPeer reviewe

EpidemicKabu a new method to identify epidemic waves and their peaks and valleys

INTRODUCTION:The dynamical behaviour of some epidemics is an oscillation between a very low and very high number of incident cases throughout the time. These oscillations are commonly called waves of the epidemic curve. The concept of epidemic waves lacks a consensual definition and a simple a methodology that can be used for many diseases. OBJECTIVE: We describe in this study EpidemicKabu a new method to identify the start and end of past epidemic waves but also their peaks and valleys. METHOD: The methodology is divided into processing of the curve, waves detection, and peaks and valleys detection. For processing the curve, we used a Gaussian kernel to diminish the noise and smooth the curve. For the detection of waves, peaks and valleys, we used the first and second derivative of the curve. The methodology is an open access library in github.com/LinaMRuizG/EpidemicKabu. We tested the method with the unCoVer data about COVID-19 daily cases reported between 2020 and 2022 for different countries. RESULTS: The results of the library are the dates of start and end of waves, peaks, and valleys. The dates are displayed on graphs and added as a new column in a dataset. CONCLUSION: This methodology is simple, easy to use, and very useful to estimate the epidemic waves and make analysis about them as the example we made. The methodology requires expert judgement to set some parameters. Future work could optimise these parameters to make the estimation more systematic