How Following the Law Helps to Fight the COVID 19 Pandemic
Mathematicians of the Higher School of Economics have calculated the effectiveness of measures taken to fight the coronavirus epidemic in different countries. They have concluded that the scale of anti-epidemic measures does not necessarily directly affect the disease rate, suggesting that one of the main reasons for this is the willingness of citizens to clearly, honestly and consistently comply with anti-epidemic measures.
Professor Fuad Aleskerov, Director of the HSE International Centre of Decision Choice and Analysis, presented the report ‘Analysis of the Pandemic and the Effectiveness of Quarantine Measures in the Largest Countries’, prepared jointly with Sergey Demin, Alexey Myachin and Vyacheslav Yakuba, at the webinar ‘Economics and Data: Opportunities for Healthcare’ on October 6th.
The researchers used data on anti-epidemic measures taken in different countries and the disease and mortality rates gathered at the University of Oxford and Johns Hopkins University.
The authors evaluated weekly data on the disease rate and measures intended to restrict foreign travel, domestic tourism, school closures, work stoppages, cancellation of public events, prohibition of mass gatherings, stopping public transport, and introduction of a stay-at-home regime from the beginning of January to September 12. Restrictions in each of these areas were divided into 3-5 gradations.
The authors of the report created an aggregate level of quarantine measures, consisting of 468 gradations and rationed from 0 to 1 (from the mildest to the most severe). 66 largest countries were divided into 5 groups depending on the disease rate, level of education and expert assessment of how law-abiding the residents were.
According to Fuad Aleskerov, researchers have not found any objective sociological or other data reflecting this indicator yet. The researchers also did not take into account the testing coverage, which can affect the detection of COVID cases in each country. To calculate the effectiveness of each of the five groups, a different equation and regression model, which took into account the impact of strict measures on the incidence rate, were developed.
According to Professor Aleskerov, there are several models for the spread of the disease. In some countries, particularly in China, incidences of COVID peaked and fell sharply after the introduction of strict measures. In Italy, Spain, Greece and Australia, there were two peaks in the incidences of COVID – in spring, when strict anti-epidemic measures did not immediately reduce the number of cases, and in summer, when the easing of quarantine measures caused a new wave of cases. Moreover, in Greece, Australia and Spain, the number of new cases exceeded the spring figures. In Australia, the re-strengthening of anti-epidemic measures from mid-June to July 11 (the index rose from 0.3 to 0.9) did not immediately lead to success: the number of new cases increased until the beginning of August, then significantly decreased. In Spain and Greece, where the summer increase was not so significant (no more than 0.5 in Greece and 0.65 in Spain), the number of cases increased in July-September.
In Italy, the aggregate level of quarantine measures up to February 22 did not exceed 0.1, by February 29th, it rose to 0.65, by March 14th – to 0.9 and on April 11th it had reached the peak value, 1. The harshest restrictions lasted a month. Then the strictness of measures quickly decreased – by June 13 to 0.2 and ranged between 0.2 and 0.35, however, the increase in the incidence in August and early September was less significant.
The experience of Germany is also interesting, here the level of restrictions even at the incidence peak in March-May did not exceed 0.65, and then decreased less noticeably, to 0.35. Finally, in Brazil, Mexico, and India, the incidence rate increased in spring and summer, despite long-term severe restrictions (an aggregate level of 0.9 to 1). It’s still unclear whether this rise can be explained only by the amount of testing.
The scale of anti-epidemic measures does not necessarily directly affect the incidence dynamics, as shown by a comparison between Russia and Sweden. In our country, the aggregate level reached 0.6 in mid-March, increased to 0.9 by mid- April, slightly decreased to 0.8 by mid-June, and significantly decreased to 0.4 only in August. However, the strengthening of measures did not prevent a peak in May in Russia. In Sweden, the index of measures never exceeded 0.4 and then dropped to 0.2. Due to these mild anti-epidemic measures, the Swedish authorities were even accused of COVID-dissidence, however, there was no incidence outburst in the Scandinavian country.
Perhaps one of the reasons is the willingness of the population to clearly, honestly and consistently comply with anti-epidemic measures. According to Fuad Aleskerov, the law-abiding index in different countries, determined by experts on a scale from 1 to 10, revealed unexpected results.
The speaker also highlighted the way education level impacts compliance with anti-COVID measures. For example, the Italians initially did not take the restrictions seriously enough, but when the situation escalated, they realized the danger and responsibly complied with anti-epidemic measures, says Aleskerov.
According to the calculations of HSE mathematicians, the most successful anti-epidemic measures were in China, where the index of their effectiveness from April to August was equal to one, or absolute. The Italian and Spanish governments learned the tragic lessons of February and March, the level of quarantine effectiveness in Italy increased from 0.02 in April to 1 in June-August, in Spain from 0.03 in April to 0.56 in July, but then began to decline again. In Germany, the efficiency level was high in the summer months (0.83 and 0.97), but began to decline in August.
According to the calculations of mathematicians, anti-epidemic measures in Russia were not effective enough. The level of their effectiveness, according to various criteria, did not exceed the level of 0.24-0.32. This is lower than in most major countries, including Japan, South Korea, and Turkey. However, the effectiveness of measures taken by the state against coronavirus in Russia was higher than in India, Brazil and, curiously, than in the United States.
See also:
‘Seeing Red Square at Night and Sharing Time with Friends from Different Countries are Moments I Will Remember for a Long Time’
Sashadhar Dutta, from India, is a second-year PhD student at the Doctoral School of Economics at the HSE University–Moscow Faculty of Mathematics. He is currently working on his PhD thesis titled ‘On Some New Bounds Connected with Recurrent Sequences Modulo Prime’ under the academic supervision of Associate Professor Ilya Vyugin. Sashadhar spoke to the HSE News Service about why HSE deserves its good reputation, what he likes about Moscow, and how his time at HSE has changed his perceptions of both Russia and his own research.
Algebra, Geometry, and AI: Russian and Vietnamese Mathematicians Discuss Current Research
A delegation of scientists from Hanoi visited the HSE Faculty of Computer Science and then took part in a Russian-Vietnamese conference in St Petersburg. The events were part of the three-year project ‘Flexibility and Computational Methods.’ Over the course of the project, the researchers have prepared joint publications and obtained new mathematical results.
Four HSE Mathematics Graduates Win Russia’s Young Mathematicians Award
The winners of the Young Mathematicians of Russia Award were announced at the 6th Conference of Russia’s Mathematical Centres, held in Kazan in late August 2026. Four of the nine award recipients are graduates of the HSE Faculty of Mathematics: Associate Professor Alexander Kalmynin, PhD students Alexander Zaitsev and Petr Kucheryavyy, and researcher Dmitry Pirozhkov.
HSE Students Win Six Gold Medals at International Mathematics Competition for University Students
Students from the HSE Faculty of Computer Science (FCS) and Faculty of Mathematics have won six gold medals at the International Mathematics Competition for University Students (IMC). HSE students also received silver and bronze medals. One of the world’s most prestigious international university mathematics competitions, IMC 2026 was held in July–August this year in Blagoevgrad, Bulgaria.
‘AI Enables Researchers to Tackle More Complex and Important Problems’
In late July 2026, Dmitry Rybin, a graduate of the HSE Faculty of Mathematics who is now working in China, used ChatGPT to disprove a longstanding mathematical hypothesis. In an interview with the HSE News Service, he discussed AI's ability to make discoveries in mathematics, reflected on his time at HSE University, and spoke about his doctoral research at the Chinese University of Hong Kong.
‘The Conference Strengthened Our Sense of Belonging to the International Mathematics Community’
From July 13 to 17, 2026, the HSE Faculty of Mathematics hosted the international conference ‘Moduli, Dynamics, and Integrability,’ bringing together leading mathematicians from Russia, the United States, China, the United Kingdom, and other countries.
Fair Division: How Mathematics Helps to Divide the Indivisible
How can items be allocated among participants so that no one feels short-changed? Alexander Karpov, Assistant Professor at the Faculty of Economic Sciences, and his Singaporean colleague, Prof. Warut Suksompong, set out to find a mathematical answer to this question. In this interview, they discuss how a model of rational preferences is constructed, why one cannot rely on a simple sum of values, and where an algorithm that asks a minimal number of questions can be useful.
HSE Students Win Gold Medals at International Mathematics Olympiad in Turkmenistan
The VI Open Mathematical Olympiad for University Students (OMOUS-2026) was held in Ashgabat, bringing together teams from Russia, Germany, Greece, Hungary, the Netherlands, Turkmenistan, Tajikistan, Uzbekistan, Iran, and the UAE. Around 600 students took part in the competition.
'Sometimes, Finding Ways to Solve Problems Feels Like Trying to Cross Mountains without a Map'
Yulia Zaitseva became interested in mathematics in third grade, when her parents enrolled her in a math club, and she now holds a PhD. In this interview with the HSE Young Scientists project, she explains what an algebraic variety is, discusses operations beyond addition and multiplication, and shares her love for Kolomenskoye Park.
Mathematician from HSE University–Nizhny Novgorod Solves Equation Considered Unsolvable in Quadratures Since 19th Century
Mathematician Ivan Remizov from HSE University–Nizhny Novgorod and the Institute for Information Transmission Problems of the Russian Academy of Sciences has made a conceptual breakthrough in the theory of differential equations. He has derived a universal formula for solving problems that had been considered unsolvable in quadratures for more than 190 years. This result fundamentally reshapes one of the oldest areas of mathematics and has potential to have important implications for fundamental physics and economics. The paper has been published in Vladikavkaz Mathematical Journal.