Evaluating Ideologies of Coronacrisis-Related Self-Isolation and Frontiers Closing by SIR Compartmental Epidemiological Model

Original article

Olga V. Valba, 

PhD, Scientist, Federal Research Center of Chemical Physics of Russian Academy of Sciences, Russia


Vladik A. Avetisov, 

PhD, Dr habil, Chief Scientist, Federal Research Centre of Chemical Physics of Russian Academy of Sciences, Russia


Alexander S. Gorsky, 

PhD, Dr habil, Leading Scientist, Institute of Information Transmission Problems of Russian Academy of Sciences, Professor, Moscow Institute of Physics and Technology, Russia


Sergei K. Nechaev,

PhD, Dr habil, Director, Interdisciplinary Scientific Centre Poncelet, CNRS UMI 2615, France

Address: Universite Paris-Sud/CNRS, LPTMS, UMR8626, 91405 Orsay, France

E-mail: sergei.nechaev@gmail.com

Article ID: 020210318

Published online: 10 November 2020

HANDLE: https://hdl.handle.net/20.500.12656/thebeacon.3.020210318

DOI: https://doi.org/10.55269/thebeacon.3.020210318


Quoting (Chicago style): Valba, Olga V., Avetisov, Vladik A., Gorsky, Alexander S., and Sergei K. Nechaev. 2020. “Evaluating Ideologies of Coronacrisis-Related Self-Isolation and Frontiers Closing by SIR Compartmental Epidemiological Model.” Beacon J Stud Ideol Ment Dimens 3, 020210318. https://doi.org/10.55269/thebeacon.3.020210318

Language: Chinese

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Soon after the beginning of the SARS-CoV-2 pandemic, controlled development of societies acquired almost all major characteristics of ideology. The creators of that ideology invented two primary ways of counteracting the spread of the novel coronavirus, “self-isolation” and frontiers closings. In our paper, we analyse the real, not imaginary effectiveness of both the ways, using SIR compartmental model. We demonstrate that, independently of ideology, a network evolutionary grown prevents the spread of the virus better than an instantly clustered network.

Key words: SARS-CoV-2, COVID-19, frontiers closing, self-isolation, lockdown, ideology, network

Extended summary in English



Almost at once counteracting SARS-CoV-2 by the governments became an ideological instrument of controlling social behaviour and relocation. Two main solutions were proposed to stop the spread of the virus, so-called "self-isolation" and closing of frontiers. The world population, once ideologically asserted that total globalisation is an unequivocal good, has been now prevailed on that the opposite process, i.e. clusterisation is the best method of curbing SARS-CoV-2 spread. Which way of clusterisation turned out to be more effectual?


In both cases the aim of clustering is to localise the illness propagation in closed community and prevent it from the spread through the entire human network. Specifically, we were interested in the question which mechanism blocks better the spread of the epidemic: the self-quarantine in local communities induced by increasing the weights of small cliques in the human network, or sharp clustering via closing of borders between arbitrary parts of the human network. In an ideal situation, when all self-isolated communities are absolutely disconnected from each other, and when the border crossings between cities and countries are totally prohibited, both protocols are equally efficient and definitely inhibit disease expansion. However, in reality, it is impossible to isolate communities completely and some fraction of cross-community connections is always present. In that case we claim that the human network clustering obtained by the self-isolation prohibits the spread of the epidemic better than the instant separation of the network into arbitrary clusters (frontiers closings with stopping air routes). Readers are invited to make their own judgement whether such a speculation seems plausible in context of the human society and to which extent. Both the ways of clusterisation require social obedience dictated by ideology and, therefore, impossible in democratic states.


We have demonstrated that the network which is evolutionary grown from a randomly generated Erdős-Rényi graph with the fixed vertex degree under the condition of maximisation of small cliques (triadic motifs) gets clustered into community clusters and the number of such communities depends on the linking probability p in the initial graph. We have also verified numerically that similar adaptive clustering occurs when triadic motifs are replaced by complete 4-cliques. Running SIR model on e-networks (evolutionary-grown networks), and in parallel, on i-networks (instantaneously created clustered networks which mimic clustered structure of e-networks, however are memory-less), we see from that e-networks prevent spread of the epidemic better than i-networks (the maximum of infected agents is lower for e-networks), while the maximum of infected agents (peak of the epidemic spread) on e-networks is shifted to later times compared to i-networks.


We have found that the clustered population e-network are scale-free, which explains some previously obtained numerical observations concerning spectral density of the adaptively grown networks. Thus, by the maximisation of number of triadic motifs in the constrained Erdős-Rényi networks we have proposed new simple mechanism of generating the scale-free graphs via the rewiring process.


The SARS-CoV-2 epidemic spreading on the scale-free networks has some specific peculiarities. In particular, the epidemic threshold almost vanishes which means that the scale-free network is bad for the epidemic suppression at the beginning of its distribution. However, once started, counteracting the epidemic can be operated on a scale-free network more effectively than on other types of networks. The new rewiring mechanism for getting scale-free behaviour can be useful for the purpose of stopping the virus spread. Anyway, by means of SIR compartmental model we showed that one ideologically loaded mechanism of stopping SARS-CoV-2 is more effective than the other, when the infection is already spread in a considerable part of population.


Therefore, the example of our study proves that mathematics may be a means of comparing ideologies in public policy, crucial for analysing the future development of societies.


© 2020 Olga V. Valba, Vladik A. Avetisov, Alexander S. Gorsky, and Sergei K. Nechaev.
Licensee The Beacon: Journal for Studying Ideologies and Mental Dimensions.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) that permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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