Prediction of COVID-19 pandemic dynamics in Russia based on simple mathematical models of epidemics

Abstract

Introduction: The COVID-19 pandemic which began in 2020 and has taken more than five million lives has become a threat to the very existence of mankind. Therefore, predicting the spread of COVID-19 in each individual country is a very urgent task. The complexity of its solution is due to the requirement for fast processing of large amounts of data and the fact that the data are mostly inaccurate and do not have the statistical properties necessary for the successful application of statistical methods. Therefore, it seems important to develop simple forecasting methods based on classical simple models of epidemiology which are only weakly sensitive to data inaccuracies. It is also important to demonstrate the feasibility of the approach in relation to the incidence data in Russia. Purpose: Obtaining forecast data based on classical simple models of epidemics, namely SIR and SEIR. Methods: For discrete versions of SIR and SEIR models, it is proposed to estimate the parameters of the models using a reduced version of the least squares method, and apply a scenario approach to the forecasting. The simplicity and a small number of parameters are the advantages of SIR and SEIR models, which is very important in the context of a lack of numerical input data and structural incompleteness of the models. Results: A forecast of the spread of COVID-19 in Russia has been built based on published data on the incidence from March 10 to April 20, 2020, and then, selectively, according to October 2020 data and October 2021 data. The results of the comparison between SIR and SEIR forecasts are presented. The same method was used to construct and present forecasts based on morbidity data in the fall of 2020 and in the fall of 2021 for Russia and for St. Petersburg. To set the parameters of the models which are difficult to determine from the official data, a scenario approach is used: the dynamics of the epidemic is analyzed for several possible values of the parameters. Practical relevance: The results obtained show that the proposed method predicts well the time of the onset of the peak incidence, despite the inaccuracy of the initial data.