“Quarantine can reduce losses”: specialist in mathematical modeling - about the COVID-19 pandemic and epidemic scenarios in Russia

- Alexander Valerievich, let's talk about the calculations of the distribution of COVID-19 in Russia and in the world. Now there is a different rate of spread of coronavirus infection. There are successes in China and South Korea, but in Europe and America a real “fire” broke out. What can already be said by the available figures, by the growth rate? Does Russia follow the Chinese scenario, the Western European one, or some other way?

- So far, we can’t talk about some pronounced scenario for our country. If we focus on the indicators of infection, mortality and recovery, then Russia is currently close to Eastern Europe and Scandinavia. Dangerous trends characteristic of Western Europe and the USA are not observed.

Almost all countries are affected by the coronavirus in the world, but a clearly negative picture is observed in about ten countries. Russia is not among them, and, subject to the necessary security measures, will not be included.

If we carefully analyze the official statistics of deaths from COVID-19, then more than half of all cases occur in Italy, Spain and the United States.

• Subject to the necessary security measures, Russia will avoid the American and Western European scenario for the development of the COVID-19 pandemic
• Reuters
• © Kai Pfaffenbach

- What mathematical models exist for forecasts of the spread of viruses and for epidemics in general?

- The mathematical apparatus for modeling epidemics is very diverse. The simplest but least accurate models are based on extrapolating the available data on incidence using regression methods, that is, studying the effect of one or more independent variables on the dependent variable. More convincing models describe the causal relationships of the onset and development of diseases in the form of a sequence of intermediate conditions.

- The media is now actively discussing the mathematical model of SEIR, finalized for the COVID-19 pandemic. What can you say about its accuracy? What models does your team use?

- The SEIR model you mentioned considers only four possible states of a person: S - healthy, E - infected during the incubation period or asymptomatic, I - infected in the active stage of the disease, and R - dead or recovered with immunity (depending on interpretation). Together with colleagues, Sergey Ivanov and Vasily Leonenko, employees of the National Center for Cognitive Development of ITMO University, we developed epidemiological models with more than twenty conditions that take into account the diverse structure of social contacts. In general, the number of conditions determines the degree of detail required to describe the pathways of a particular disease.

• With COVID-19, measurement and data acquisition methods are limited
• Flickr
• © NIAID

- Is it possible to say that your calculation model is the most effective?

- Any mathematical model is an abstraction that only partially reflects the properties of real-world objects. In the situation with COVID-19, the possibilities of measurement and data collection methods are limited. Due to the uncertainty, the complication of the structure of the model itself does not lead to an increase in the quality of forecasts - as long as they all fit into a fairly wide probability interval. Therefore, it is possible to speak about the prognostic effectiveness of a particular model only according to the “Hamburg account” when it is all over.

- What factors have the greatest weight in the calculations? Health system preparedness, population density, citizens responsibility, decisive actions of the authorities?

- There is no single answer to this question. In general, for pathogens transmitted by airborne droplets and contact-household routes, which include COVID-19, the main factors are the biological nature of the disease: virulence, the duration of the incubation and infectious periods, and the mortality rate. Also important are the properties of the population in which the disease occurs: total strength, immunity level, age structure, and number of contacts.

Epidemiological models are not enough for a quantitative analysis of factors, because the spread of infection is a social process. This is especially important for coronavirus, since it is distributed mainly by asymptomatic carriers.

- Are you using any additional models?

- In parallel with the epidemiological model, a model is used that describes the daily life and activity of the population, the so-called virtual society. We developed such a model at the Institute of Design and Urbanism at ITMO University for St. Petersburg with the support of the Russian Science Foundation. It allows you to reproduce the distribution of the population density of the city during the day and evaluate the structure of contacts between people at home, at work, in the store, in transport.

- Are there models for calculating the effectiveness of regimes of different severity: restrictions on movement, self-isolation, quarantine and emergency?

- Such calculations are performed by different scientific teams and usually do not coincide quantitatively. At the same time, they demonstrate a clear trend - the fewer contacts, the less infected. However, on the basis of the virtual society model, various social mechanisms of such contacts can be controlled.

In digital form, you can "lock" the townspeople at home, "restrict" traffic, "close" the entrance to the city. The effectiveness of measures is determined by their influence on changing the structure and intensity of ties in society. It is not necessary to completely destroy all contacts. It is enough to ensure the division of society into groups, the number of connections within which is significantly less than between them. This can not only slow down, but stop the course of the epidemic, as was observed in China.

- How does the social activity of an individual affect the overall picture?

- Reception of grouping works effectively even against super-distributors and quarantine violators. They will be unable to significantly affect the epidemiological situation as a whole. However, due to the insufficient knowledge of the coronavirus, it is difficult to determine the characteristics of the structure of social connections that limit the development of the epidemic. Moreover, judging by similar cases and the experience of other countries, the measures taken in Russia allow us to hope for the best.

• Street disinfection in the Leningrad region
• RIA News
• © Alexander Halperin

- How are the consequences calculated? When will the peak, recession of the epidemic in Russia?

- The standard picture for viral infections usually gives from one to three months for the entire epidemic cycle, provided that there are no massive “deliveries”. There is no reason to believe that the picture in Russia will be different. To configure the model according to domestic data, it is necessary to see the effects of isolation measures, which require at least two weeks to evaluate.

The epidemic is on the decline when every infected person infects less than one healthy one. This process is inevitable, first of all, for biological reasons, such as the gradual immunization of society or the weakening of the virus itself, which is completely unprofitable for its survival and spread.

Isolation and quarantine can regulate this process and reduce losses for society as a whole. At the same time, one should not forget about the existence of a background level of SARS, which is formed by numerous "relatives" of this virus. Perhaps this very background level, which is quite high in Russia, is a natural defense of citizens from the dire consequences of the epidemic.

- Are there any models for calculating the occurrence of such disasters, their warning? Can your work help to eliminate such threats at the start?

- The very fact of the occurrence of such disasters is difficult to identify in advance. Usually very general models of the evolution of complex systems are used for this. They are described by nonlinear differential equations and are sometimes able to demonstrate chaotic behavior, which is considered the beginning of a disaster: an epidemic, financial crisis or revolution. The main attention is paid to the early detection of the so-called critical points when the system is in a transitional state and there is enough light push to send it into a crisis that cannot be stopped.

This area is new and so far requires an individual approach for each problem. The key difficulty is that the equations themselves describing the evolution of a system are usually unknown. The question arises whether it is possible to build them on the basis of retrospective data. In general, this can be done using artificial intelligence technologies that allow you to "grow" such equations on data using evolutionary algorithms. This can be done quite clearly for influenza and SARS, but for COVID-19, enough data has not yet been accumulated, since epidemics in most countries have not reached a peak. This is our scientific agenda for the near future.

- What can be said about the coronavirus pandemic in terms of your area of ​​expertise? What type of critical phenomena in complex social systems does it belong to? What are its “strengths” and “weaknesses”?

- First of all, in the situation with COVID-19, the problem of juxtaposing the individual and society was clearly manifested. In all countries, self-isolation regulations are not always and not always followed. At the same time, the consolidation of society in terms of minimizing social ties makes it possible to compensate for the actions of violators, and the epidemic is spreading on a much smaller scale. However, no one should relax, since it is the violators who are the first to become victims of the infection that suffer from such actions.

Another trend that we have encountered follows from the logic of the science of global systems. It describes cascades of critical effects that occur in several related complex systems. For example, when the rapid spread of the epidemic through social networks causes a decrease in logistic activity and a simultaneous overload of digital networks.

As a result, “the trouble does not come alone”: there is a risk of staying home without the Internet, which is a critical infrastructure. The main difficulty in identifying such situations in advance is that they never occur in everyday operation, but arise only in critical states of complex systems. I believe the COVID-19 pandemic will provide new experience for the design of distributed control systems for complex socio-technical infrastructures.