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1 Drawing Transmission Graphs for COVID-19 in the Perspective Of medRxiv preprint doi: https://doi.org/10.1101/2020.08.11.20172908; this version posted August 14, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission. Drawing transmission graphs for COVID-19 in the perspective of network science N. GÜRSAKAL1 B. BATMAZ 2 G. AKTUNA 3 Name of department(s) and institution(s) 1.Fenerbahçe University, Faculty of Economics and Administrative Sciences 2.Anadolu University, Open Education Faculty, 3.Hacettepe University, Public Health Institute, ABSTRACT When we consider a probability distribution about how many COVID-19 infected people will transmit the disease, two points become important. First, there should be super-spreaders in these distributions/networks and secondly, the Pareto principle should be valid in these distributions/networks. When we accept that these two points are valid, the distribution of transmission becomes a discrete Pareto distribution, which is a kind of power law. Having such a transmission distribution, then we can simulate COVID-19 networks and find super- spreaders using the centricity measurements in these networks. In this research, in the first we transformed a transmission distribution of statistics and epidemiology into a transmission network of network science and secondly we try to determine who the super-spreaders are by using this network and eigenvalue centrality measure. We underline that determination of transmission probability distribution is a very important point in the analysis of the epidemic and determining the precautions to be taken. NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice. 1 medRxiv preprint doi: https://doi.org/10.1101/2020.08.11.20172908; this version posted August 14, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission. INTRODUCTION The first half of 2020 passed with the whole world dealing with the COVID-19 outbreak. First, many countries implemented lockdown, and then reopening came to the agenda. However, at the time of writing this article, there was an important increase in the number of infections all over the world and we would probably spend the second half of the year dealing with the COVID-19 issue and lockdowns again. The fact that COVID-19 is a relatively new virus also challenges scientists and scientific analysis have to navigate the uncharted territories [1]. This article attempts to establish a link between the fields of statistics, network science and epidemiology using an interdisciplinary approach. From a micro point of view, this connection, which was tried to be established, was made by converting transmission distribution of statistics and epidemiology into a transmission network of network science. From a micro point of view, the study also tries to contribute to efforts to stop the epidemic by identifying who the super spreaders are, and then by researching and identifying their various characteristics. In analyzing COVID-19 outbreak, most of the times, instead of focusing on a transmission probability distribution; R0 value as an average or median have been used and super- spreaders are not taking into account. But the extreme values make a long tail for this distribution and rare infection events determine the shape of this distribution. It has been seen that different R0 numbers were obtained in the literature for COVID-19 and some authors try to emphasize that 80% of cases are infected by a group of 20%. But most of the times, the fact that 80% of the infection is carried out by a 20% group is often not considered and most of the analysis begin with a R0 reproduction number. Nearly all of the COVID-19 studies begin with the determination of reproduction number R0. For example, if a disease has an R0 of 15, a person who has the disease will transmit it to an average of 15 other people. This coefficient is important because also we use this number to see the severity of outbreak and this number is also used as an epidemic threshold parameter. 2 medRxiv preprint doi: https://doi.org/10.1101/2020.08.11.20172908; this version posted August 14, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission. Different methods are being used to determine this number. First of all, this number can be calculated as: R0=Contact rate*Probability of infection*Infection period Secondly, this coefficient can be calculated using “attack rate” and attack rate is the percentage of the population eventually infected. Thirdly we can estimate R0 using formula: Ro = Life expectancy Average age And fourthly we can estimate Ro using exponential growth rate. “Since the R0 has a key role in measuring the transmission of diseases and is crucial in preventing epidemics, thus it is important to know which methods and formulas to apply to estimate R0 and have better performance” [2]. But we know that different methods give different results [3] and most of the times in scientific articles which method has been used is not mentioned. Besides, sometimes R0 value is given as a median; for example, it is expressed as, “We estimated that the median of estimated R0 is 5.7 (95% CI of 3.8–8.9)” [4] and this may lead us to some confusion too. “The emerging picture for epidemic spreading in complex networks emphasizes the role of topology in epidemic modeling” [5]. Disease transmission networks have the motifs of transmission stories. One of the most important ways to avoid contamination is to have information about how this transmission happens. The main purpose of this study is to develop a simple method that will make it easier for us to look at the COVID-19 issue from the network science window. And focusing on the interplay between network theory, statistics and epidemiology [6] In this simple method, first we determine a transmission probability distribution and secondly simulating this probability distribution we can draw a transmission graph and try to understand the process contamination using this graph. We should underline that determination of transmission probability distribution is a very important point in the analysis of the epidemic and 3 medRxiv preprint doi: https://doi.org/10.1101/2020.08.11.20172908; this version posted August 14, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission. determining the precautions to be taken. Having such a graph, also we may compute many network measures and use this measures in our decision process. Our study, which started with an introduction, includes a literature review on the R0 values calculated for COVID-19. The following section examines the phenomenon of super- spreaders. Then, the issues of generating the values obtained by simulating a discrete Pareto distribution and drawing and interpreting the transmission network are included. The study is completed with a discussion section. R0 values calculated for COVID-19 COVID-19 transmission is strongly heterogeneous [7]. A high degree of individual-level variation in the transmission of COVID-19 has been expressed and consensus range of R0 was found within the interval of 2-3 [8]. Results show that there was probably substantial variation in SARS-CoV-2 transmission over time after control measures were introduced. In the beginning of outbreak in Wuhan R0 median daily reproduction number changes from 2.35 to 1.05 in only one week. But even in the before the travel restrictions period it was found that, median daily R0 changes between 1.6 and 2.6 in Wuhan [9]. In the early days of outbreak in Wuhan another study estimates R at 0.24 (95% CrI: 0.01–1.38) for market-to- human transmission and 2.37 (95% CrI: 2.08–2.71) for human-to-human transmission [10]. And also in another paper it was stated that, “We identified four major clusters and estimated the reproduction number at 1.5 (95% CI: 1.4–1.6)” [11]. “We modelled the transmission process in the Republic of Korea and Italy with a stochastic model, and estimated the basic reproduction number R0 as 2.6 (95% CI: 2.3–2.9) or 3.2 (95% CI: 2.9–3.5) in the Republic of Korea, under the assumption that the exponential growth starting on 31 January or 5 February 2020, and 2.6 (95% CI: 2.3–2.9) or 3.3 (95% CI: 3.0–3.6) in Italy, under the assumption that the exponential growth starting on 5 February or 10 February 2020, respectively.” [12]. From these lines we learn that Ro is between 2.6 -3.2 for Republic of Korea and 2.6-3.3 for Italy. Transmission was modelled as a geometric random walk process, or negative binomial offspring distribution is used to calculate the probabilities: “Once we had estimated Rt , we 4 medRxiv preprint doi: https://doi.org/10.1101/2020.08.11.20172908; this version posted August 14, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
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