MATHEMATICAL MODEL FOR MEDIUM-TERM COVID-19 FORECASTS IN KAZAKHSTAN

Abstract

In this paper has been formulated and solved the problem of identifying unknown parameters of the mathematical model describing the spread of COVID-19 infection in Kazakhstan, based on additional statistical information about infected, recovered and fatal cases. The considered model, which is part of the family of modified models based on the SIR model developed by W. Kermak and A. McKendrick in 1927, is presented as a system of 5 nonlinear ordinary differential equations describing the variational transition of individuals from one group to another. By solving the inverse problem, reduced to solving the optimization problem of minimizing the functional, using the differential evolution algorithm proposed by Rainer Storn and Kenneth Price in 1995 on the basis of simple evolutionary problems in biology, the model parameters were refined and made a forecast and predicted a peak of infected, recovered and deaths among the population of the country. The differential evolution algorithm includes the generation of populations of probable solutions randomly created in a predetermined space, sampling of the algorithm's stopping criterion, mutation, crossing and selection.