Russian mathematicians develop a new model for predicting epidemics based on precedents

December 09, 2020

Scientists of the Intelligent Logistics Centre at St Petersburg University have developed a new Case-Based Rate Reasoning (CBRR) model for predicting the dynamics of epidemics. Using this method, the researchers are preparing forecasts for the spread of COVID-19 in Russia. The predictions are based on data on the dynamics of the epidemic in countries where the disease was recorded earlier.

The scientists faced a challenge when they began to build their first forecasts in April-May 2020: all available models for mathematical forecasting the dynamics of epidemics did not work for COVID-19.

'In April-May 2020, there were no statistics on the dynamics of the new virus yet, while such statistics are available for viruses already known to mankind. The class of models available at that time was therefore not applicable for forecasting the dynamics of the epidemic. It was necessary to develop a new approach and a new CBRR model. Its feature is that, to predict the epidemic evolution in Russia, it uses data on the dynamics of the spread of the new coronavirus in countries where the epidemic began earlier than in our country,' said Professor Victor Zakharov, Head of the Intelligent Logistics Centre at St Petersburg University, Head of the Department of Mathematical Modelling of Energy Systems at St Petersburg University, Doctor of Physics and Mathematics.

Having established the new model for Russia as a whole, the scientists started to update their forecasts for St Petersburg and Moscow on a weekly basis (their forecasts are available on the website of the Intelligent Logistics Centre at St Petersburg University). According to the latest forecasts, in Russia the daily increase in new cases of COVID-19 over the past two weeks ranges from 24,000 to 27,000. On 3 December 2020, for the first time this figure exceeded 28,000. If this level of growth continues for 7 to 10 days, Russia will flatten the curve of the number of new cases. If it then begins to decrease, scientists believe that Russia may peak on 21-22 December 2020 in the number of active cases: that is according to the number of sick people on a particular day. On these days, the number of infected people in the country as a whole could range from 514,000 to 517,000. These values must be taken into account in order to understand the load level of the health care system and plan its work for the future.

The new CBRR model is built on an iterative approach: the data on which the predictions are based is updated in real time for a period of 2-3 weeks. Thus, the real course of the epidemic over the last analysed time period makes it possible to calculate more accurately the forecast of its dynamics in the near future. 'The forecast for Russia and the United States in the spring was built 2-3 weeks ahead of the current time. In the forecasts for St Petersburg and Moscow, we rely on the data of the previous days (2-3 weeks) and make predictions using the same model, but adjusted for these data,' said Victor Zakharov.

'The developed CBRR model includes an iterative procedure for the heuristic selection of interval lengths, a set of values of percentage growth, and other significant parameters. These include: peaks in terms of the increase in new cases and possible periods of peak height; and peaks in terms of the number of active cases. A significant component of the iterative procedure is the formation of the chain of countries with epidemic spread (Epidemic Spreading Chain, ESC), which includes several countries ranked by the time they reach the same levels of the selected parameters. The country for which the forecast is being built is called the Country Follower, the rest of the countries we refer to as Country Predecessors,' added Victor Zakharov.

Professor Zakharov noted that for the correct tuning of the model, it is necessary that the ESC countries use relatively identical measures against the epidemic spread: quarantine, self-isolation, social distancing, and the like. As he clarified, the epidemic in the Russian Federation, the country-follower, is characterised by a later date when the same percentage growth rates were reached in comparison with other countries. 'Based on this fact, when modelling and predicting the dynamics of the epidemic in Russia, we included Italy, Spain, Great Britain, and France as country-predecessors in the ESC chain. The sequentially generated evolution trajectory of the statistical data on the epidemic, for example, the total number of infected people, is compared with the actual statistical data,' said Victor Zakharov.

St. Petersburg State University

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