Mathematical Modeling and Short-Term Forecasting of the COVID-19 Epidemic in Bulgaria: SEIRS Model with Vaccination

Svetozar Margenov, Nedyu Popivanov, Iva Ugrinova and Tsvetan Hristov
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Svetozar Margenov: Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
Nedyu Popivanov: Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
Iva Ugrinova: Institute of Molecular Biology, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
Tsvetan Hristov: Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”, 1164 Sofia, Bulgaria

Mathematics, 2022, vol. 10, issue 15, 1-28

Abstract: Data from the World Health Organization indicate that Bulgaria has the second-highest COVID-19 mortality rate in the world and the lowest vaccination rate in the European Union. In this context, to find the crucial epidemiological parameters that characterize the ongoing pandemic in Bulgaria, we introduce an extended SEIRS model with time-dependent coefficients. In addition to this, vaccination and vital dynamics are included in the model. We construct an appropriate Cauchy problem for a system of nonlinear ordinary differential equations and prove that its unique solution possesses some biologically reasonable features. Furthermore, we propose a numerical scheme and give an algorithm for the parameters identification in the obtained discrete problem. We show that the found values are close to the parameters values in the original differential problem. Based on the presented analysis, we develop a strategy for short-term prediction of the spread of the pandemic among the host population. The proposed model, as well as the methods and algorithms for parameters identification and forecasting, could be applied to COVID-19 data in every single country in the world.

Keywords: COVID-19 pandemic; time-dependent SEIRS model; Cauchy problem for non-linear ODE; parameters identification; inverse problems; vaccination; vital dynamics; forecasting (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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