St Petersburg University scientists develop mathematical model to predict epidemics
Mathematicians from St Petersburg University have optimised the previously developed model for forecasting the COVID-19 pandemic spread patterns. The optimised model can be used to predict the spread of any epidemic. After a month of continuous observation, the model can predict with high accuracy the number of active cases in the following three to four weeks. The University mathematicians applied this model to predict the spread of new viruses using the example of the COVID-19 pandemic.
In 2021-2022, a team of researchers from the Centre for Dynamic Process and System Analysis at St Petersburg University developed a new approach to the study of inflow and outflow systems with stochastic variables and a new methodology for predicting the dynamics of such systems. Thus, the scientists were able to identify new peaks in the incidence of the disease and the key indicators. The model was modified based on the hypothesis of the natural character of the multiple factors that influence the dynamics of these processes. Accordingly, the St Petersburg University mathematicians employed the dynamic game principles against nature as a mathematical model of decision-making in predictive modelling. It turned out that the dynamics of the spread of new viruses, as well as the dynamics of population growth within a specific country or globally, can be described using the stochastic CIR model, i.e. the Cox-Ingersoll-Ross model with random parameters.
The results of applications of the developed methodology for dynamic forecasting of the active COVID-19 cases in St Petersburg and Moscow were presented at the plenary session of the scientific and practical interdisciplinary conference "Human capital: education, labour, employment in modern society", dedicated to the 300th anniversary of St Petersburg University. The results were presented by Victor Zakharov, Head of the Centre for Dynamic Process and System Analysis at St Petersburg University, Professor in the Department of Mathematical Modelling of Energetic Systems at St Petersburg University.
The practical applicability of the developed methodology was tested in many numerical experiments, performed to generate retrospective forecasts of the process dynamics based on past statistics.
The mathematical model developed by St Petersburg researchers predicted COVID-19 incidence rates in Russia to decrease to 25,000 cases by autumn 2022.
"We found that the key variables in stochastic dynamic traffic flow systems can have quite predictable dynamics that can be detected and described by analysing the dynamics of pre-existing data. For instance, for the COVID-19 pandemic, data on the percentage increase in the first-wave cases enabled to significantly reduce the uncertainty about the following development of the epidemic and predict further rises and falls in incidence rates. Given the biological nature of viruses, we can assume that predictability of stochastic input variables in CIR models can be applied to all new viruses and virus mutations," said Victor Zakharov, Professor in the Department of Mathematical Modelling of Energy Systems at St Petersburg University.
Thus, based on the ongoing analysis of statistical data and mathematically modelled dynamic trends in the percentage change in the number of active and closed cases, the University mathematicians can predict with a high degree of accuracy, in real time, the current number of active cases over a forecast horizon of three to four weeks. Such forecasts can provide a methodological basis for planning the regional healthcare system interventions in times of viral epidemics, including both novel and previously recognised viruses.