Computing the COVID-19 Basic and Effective Reproduction Numbers Using Actual Data: SEIRS Model with Vaccination and Hospitalization

A novel time-dependent deterministic SEIRS model, extended with vaccination, hospitalization, and vital dynamics, is introduced. Time-varying basic and effective reproduction numbers associated with this model are defined, which are crucial metrics in understanding epidemic dynamics. Furthermore, a...

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Main Authors: Svetozar Margenov, Nedyu Popivanov, Tsvetan Hristov, Veneta Koleva
Format: Article
Language:English
Published: MDPI AG 2024-12-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/12/24/3998
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author Svetozar Margenov
Nedyu Popivanov
Tsvetan Hristov
Veneta Koleva
author_facet Svetozar Margenov
Nedyu Popivanov
Tsvetan Hristov
Veneta Koleva
author_sort Svetozar Margenov
collection DOAJ
description A novel time-dependent deterministic SEIRS model, extended with vaccination, hospitalization, and vital dynamics, is introduced. Time-varying basic and effective reproduction numbers associated with this model are defined, which are crucial metrics in understanding epidemic dynamics. Furthermore, a parameter identification approach has been used to develop a numerical method to compute these numbers for long-term epidemics. We analyze the actual COVID-19 data from the USA, Italy, and Bulgaria to solve appropriate inverse problems and gain an understanding of the time evolution behavior of the basic and effective reproduction numbers. Moreover, an insightful comparison of key coronavirus data and epidemiological parameters across these countries has been conducted. For this purpose, while the basic and effective reproduction numbers provide insights into the virus transmission potential, we propose data-driven criteria for assessing the actual realization of the transmission potential of the SARS-CoV-2 virus and the effectiveness of the applied restrictive measures. To obtain these results, we conduct a mathematical analysis to demonstrate various biological properties of the new differential model, including non-negativity, boundedness, existence, and uniqueness of the solution. The new model and the associated numerical simulation tools proposed herein could be applied to COVID-19 data in any country worldwide and hold a promising potential for the transmission capacity and impact of the virus.
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spelling doaj-art-625afb05e94d49dea88c451d0b02fc1d2025-08-20T02:57:14ZengMDPI AGMathematics2227-73902024-12-011224399810.3390/math12243998Computing the COVID-19 Basic and Effective Reproduction Numbers Using Actual Data: SEIRS Model with Vaccination and HospitalizationSvetozar Margenov0Nedyu Popivanov1Tsvetan Hristov2Veneta Koleva3Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, 1113 Sofia, BulgariaInstitute of Information and Communication Technologies, Bulgarian Academy of Sciences, 1113 Sofia, BulgariaFaculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”, 1164 Sofia, BulgariaFaculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”, 1164 Sofia, BulgariaA novel time-dependent deterministic SEIRS model, extended with vaccination, hospitalization, and vital dynamics, is introduced. Time-varying basic and effective reproduction numbers associated with this model are defined, which are crucial metrics in understanding epidemic dynamics. Furthermore, a parameter identification approach has been used to develop a numerical method to compute these numbers for long-term epidemics. We analyze the actual COVID-19 data from the USA, Italy, and Bulgaria to solve appropriate inverse problems and gain an understanding of the time evolution behavior of the basic and effective reproduction numbers. Moreover, an insightful comparison of key coronavirus data and epidemiological parameters across these countries has been conducted. For this purpose, while the basic and effective reproduction numbers provide insights into the virus transmission potential, we propose data-driven criteria for assessing the actual realization of the transmission potential of the SARS-CoV-2 virus and the effectiveness of the applied restrictive measures. To obtain these results, we conduct a mathematical analysis to demonstrate various biological properties of the new differential model, including non-negativity, boundedness, existence, and uniqueness of the solution. The new model and the associated numerical simulation tools proposed herein could be applied to COVID-19 data in any country worldwide and hold a promising potential for the transmission capacity and impact of the virus.https://www.mdpi.com/2227-7390/12/24/3998SARS-CoV-2COVID-19 pandemicvaccinationhospitalizationICUvital dynamics
spellingShingle Svetozar Margenov
Nedyu Popivanov
Tsvetan Hristov
Veneta Koleva
Computing the COVID-19 Basic and Effective Reproduction Numbers Using Actual Data: SEIRS Model with Vaccination and Hospitalization
Mathematics
SARS-CoV-2
COVID-19 pandemic
vaccination
hospitalization
ICU
vital dynamics
title Computing the COVID-19 Basic and Effective Reproduction Numbers Using Actual Data: SEIRS Model with Vaccination and Hospitalization
title_full Computing the COVID-19 Basic and Effective Reproduction Numbers Using Actual Data: SEIRS Model with Vaccination and Hospitalization
title_fullStr Computing the COVID-19 Basic and Effective Reproduction Numbers Using Actual Data: SEIRS Model with Vaccination and Hospitalization
title_full_unstemmed Computing the COVID-19 Basic and Effective Reproduction Numbers Using Actual Data: SEIRS Model with Vaccination and Hospitalization
title_short Computing the COVID-19 Basic and Effective Reproduction Numbers Using Actual Data: SEIRS Model with Vaccination and Hospitalization
title_sort computing the covid 19 basic and effective reproduction numbers using actual data seirs model with vaccination and hospitalization
topic SARS-CoV-2
COVID-19 pandemic
vaccination
hospitalization
ICU
vital dynamics
url https://www.mdpi.com/2227-7390/12/24/3998
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AT nedyupopivanov computingthecovid19basicandeffectivereproductionnumbersusingactualdataseirsmodelwithvaccinationandhospitalization
AT tsvetanhristov computingthecovid19basicandeffectivereproductionnumbersusingactualdataseirsmodelwithvaccinationandhospitalization
AT venetakoleva computingthecovid19basicandeffectivereproductionnumbersusingactualdataseirsmodelwithvaccinationandhospitalization