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Drawing Transmission Graphs for COVID-19 in the Perspective of Network Science Cambridge.Org/Hyg Epidemiology and Infection Drawing transmission graphs for COVID-19 in the perspective of network science cambridge.org/hyg N. Gürsakal1,B.Batmaz2 and G. Aktuna3 1Faculty of Economics and Administrative Sciences, Fenerbahçe University, Istanbul, Turkey; 2Open Education Original Paper 3 Faculty, Anadolu University, Eskisehir, Turkey and Public Health Institute, Hacettepe University, Ankara, Turkey Cite this article: Gürsakal N, Batmaz B, Aktuna G (2020). Drawing transmission graphs Abstract for COVID-19 in the perspective of network science. Epidemiology and Infection 148, e269, When we consider a probability distribution about how many COVID-19-infected people will 1–7. https://doi.org/10.1017/ transmit the disease, two points become important. First, there could be super-spreaders in S0950268820002654 these distributions/networks and second, the Pareto principle could be valid in these distribu- tions/networks regarding estimation that 20% of cases were responsible for 80% of local trans- Received: 20 July 2020 Revised: 28 September 2020 mission. When we accept that these two points are valid, the distribution of transmission Accepted: 28 October 2020 becomes a discrete Pareto distribution, which is a kind of power law. Having such a transmis- sion distribution, then we can simulate COVID-19 networks and find super-spreaders using Key words: the centricity measurements in these networks. In this research, in the first we transformed a COVID-19; network science; reproduction number; super-spreader; transmission graphs transmission distribution of statistics and epidemiology into a transmission network of net- work science and second we try to determine who the super-spreaders are by using this net- Author for correspondence: work and eigenvalue centrality measure. We underline that determination of transmission G. Aktuna, E-mail: [email protected] probability distribution is a very important point in the analysis of the epidemic and deter- mining the precautions to be taken. 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 paper, 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 paper 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 connec- tion, 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. COVID-19-positive people who have strong social connections and do not consider social distancing are potential super-spreaders. Of course, not everyone included in this definition will be super-spreaders, and this definition will only include potentially super-spreaders. In such a case, let us assume that we are at zero point in time, before the pandemic has started. Such a social network will show us that no one is infected yet, but who is disregarding social distance, and who has strong social connections, both ignoring social distance. This type of social network will give us clues about who could be potentially infectious and who might be super-spreaders. We can call this network the pre-pandemic network, as well as the ‘pre-analysis network’ at any time in the pandemic. During the pandemic, we can create a second ‘pandemic network’ later than when we got the pre-analysis net- work, this time to give us social connections of the infected, the non-infected and the super-spreaders. © The Author(s), 2020. Published by As a result, we will have two networks: the first one is the ‘pre-pandemic’ or ‘pre-analysis’ Cambridge University Press. This is an Open network and the second one is the ‘pandemic network’. It is possible to think of the first of Access article, distributed under the terms of these two networks as a funnel. Also, people who are not potentially viewed as super-spreaders the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), in our first network may become super-spreaders over time. A detailed comparison of these which permits unrestricted re-use, two networks will teach us a lot. Even if it seems surprising and futuristic at first, this kind distribution, and reproduction in any medium, of pro activity can be used to determine which people will be super-spreaders using networks. provided the original work is properly cited. In an age when people can’t live without cell phones, forming both of these networks will not be too difficult for authorities. It is now a known fact that it is not difficult to see who is close to whom with the signals emitted by mobile phones. Although at first it seems that per- sonal privacy will prevent the acquisition of such networks, we know that this is not a problem in some countries such as China. Downloaded from https://www.cambridge.org/core. IP address: 170.106.40.219, on 30 Sep 2021 at 16:10:36, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0950268820002654 2 N. Gürsakal et al. ‘Mobile location data provides a granular solution for con- around 40 and Washington State more than 30 people have sumer understanding. Combining this understanding with other been infected and we should also add that there are no big differ- datasets are helping to solve business problems and achieve ences in the dates of the events as seen from footnote [7]. goals across many different industries’. The sad and tragically Looking at the outbreaks in history, it can be seen that the phe- funny thing is that although such data are available for consumer nomenon of super-spreaders is not new. ‘We examine the distri- estimates, they are not used in the case of COVID-19. Also, it is bution of fatalities from major pandemics in history (spanning not easy for ordinary scientists to access such big data, and the about 2500 years), and build a statistical picture of their tail prop- authors of this paper, despite their best efforts, were unable to erties. Using tools from Extreme Value Theory (EVT), we show access even small data, not big data. Under these circumstances, for that the distribution of the victims of infectious diseases is they determined the following method and applied this method. extremely fat-tailed’ [8]. Susceptible hosts within a population Defining a method, a way of doing something with a definite had not equal chances of becoming infected. Although ‘it is still plan, we can list our phases as follows: unclear why certain individuals infect disproportionately large numbers of secondary contacts’ [9]. If we have extreme transmit- ‘ (1) Determination of an appropriate Pareto distribution that can ters, then the practice of relying on an average R0 in dynamic dis- explain the transmission with statistical analysis. ease models can obscure considerable individual variation in (2) Drawing the COVID-19 transmission network using the dis- infectiousness’ [10]. tribution obtained in the first stage, generating random Heterogeneities in the transmission of infectious agents are numbers. known since the end of 1990s [11]. We can define the phenom- (3) Identifying super-spreaders in the transmission network by enon of super-spreaders in the framework of network science as network centrality measure. follows: ‘The super-spreaders are the nodes in a network that can maximize their impacts on other nodes, as in the case of However, what is ideal for them is to identify and compare the information spreading or virus propagation’ [12]. This definition two networks they call ‘pre-pandemic’ and ‘pandemic’ networks. reminds us the outlier concept of statistics. But super-spreaders If the two aforementioned networks are created and compared, are not outliers that can be discarded from analysis, ‘In this then the first step of the method used in the paper will be framework, super-spreading events (SSEs) are not exceptional unnecessary. Obviously, the first stage of the method used in events, but important realizations from the right-hand tail of a the paper is just a facility used to overcome the difficulties in find- distribution’ [13]. ing data. One of the most important features of COVID-19 in con- In analysing COVID-19 outbreak, most of the times, instead of tamination in society is the Pareto principle created by super- focusing on a transmission probability distribution; R0 value as an spreaders. Super-spreaders transmit the disease to a large num- average or median have been used and super-spreaders are not berofpeopleinanoutlier-likemanner,resultinginfewpeople taking into account. But the extreme values make a long tail for transmitting the disease to a large number of people, and as a this distribution and rare infection events determine the shape result we have a transmission distribution as a power-law of this distribution. distribution. ‘ Since the R0 has a key role in measuring the transmission of Since many years there has been a debate that power-law for- diseases and is crucial in preventing epidemics, thus it is import- mulations are performed better than others in infectious diseases ant to know which methods and formulas to apply to estimate R0 [14], researchers are beginning to come to a consensus that cor- and have better performance’ [2].
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