Predictions of COVID-19 Pandemic Dynamics in Ukraine and Qatar Based on Generalized SIR Model

Abstract

Background. To simulate how the number of COVID-19 cases increases versus time, various data sets and different mathematical models can be used. Since there are some differences in statistical data, the results of simulations can be different. Complex mathematical models contain many unknown parameters, the values ​​of which must be determined using a limited number of observations of the disease over time. Even long-term monitoring of the epidemic may not provide reliable estimates of the model parameters due to the constant change of testing conditions, isolation of infected, quarantine conditions, pathogen mutations, vaccinations, etc. Therefore, simpler approaches are necessary. In particular, previous simulations of the COVID-19 epidemic dynamics in Ukraine were based on smoothing of the dependence of the number of cases on time and the generalized SIR (susceptible–infected–removed) model. These approaches allowed detecting the pandemic waves and calculating adequate predictions of their duration and final sizes. In particular, eight waves of the COVID-19 pandemic in Ukraine were investigated. Objective. We aimed to detect the changes in the pandemic dynamics and present the results of SIR simu­lations based on Ukrainian national statistics and data reported by Johns Hopkins University (JHU) for Ukraine and Qatar. Methods. In this study we use the smoothing method for the dependences of the number of cases on time, the generalized SIR model for the dynamics of any epidemic wave, the exact solution of the linear differential equations, and statistical approach for the model parameter identification developed before. Results. The optimal values of the SIR model parameters were calculated and some predictions about final sizes and durations of the epidemics are presented. Corresponding SIR curves are shown and compared with the real numbers of cases. Conclusions. Unfortunately, the forecasts are not very optimistic: in Ukraine, new cases will not stop appearing until June–July 2021; in Qatar, new cases are likely to appear throughout 2021. The expected long duration of the pandemic forces us to be careful and in solidarity. Probably the presented results could be useful in order to estimate the efficiency of vaccinations.