Analytical and Numerical Investigation of the SIR Mathematical Model

This is a theoretical study of the SIR model — a popular mathematical model of the propagation of infectious diseases. We construct a solution of the Cauchy problem for a system of two ordinary differential equations describing in integral form the concentration dynamics of infected and recovered in...

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Autores principales: Semendyaeva, N. L., Orlov, M. V., Rui, Tang, Enping, Yang
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2023
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10074335/
http://dx.doi.org/10.1007/s10598-023-09572-7
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author Semendyaeva, N. L.
Orlov, M. V.
Rui, Tang
Enping, Yang
author_facet Semendyaeva, N. L.
Orlov, M. V.
Rui, Tang
Enping, Yang
author_sort Semendyaeva, N. L.
collection PubMed
description This is a theoretical study of the SIR model — a popular mathematical model of the propagation of infectious diseases. We construct a solution of the Cauchy problem for a system of two ordinary differential equations describing in integral form the concentration dynamics of infected and recovered individuals in an immune population. A qualitative analysis is carried out of the stationary system states using the Lyapunov function. An expression is obtained for the coordinates of the equilibrium points in terms of the Lambert W-function for arbitrary initial values. The application of the SIR model for the description of COVID-19 propagation dynamic is demonstrated.
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spelling pubmed-100743352023-04-05 Analytical and Numerical Investigation of the SIR Mathematical Model Semendyaeva, N. L. Orlov, M. V. Rui, Tang Enping, Yang Comput Math Model Article This is a theoretical study of the SIR model — a popular mathematical model of the propagation of infectious diseases. We construct a solution of the Cauchy problem for a system of two ordinary differential equations describing in integral form the concentration dynamics of infected and recovered individuals in an immune population. A qualitative analysis is carried out of the stationary system states using the Lyapunov function. An expression is obtained for the coordinates of the equilibrium points in terms of the Lambert W-function for arbitrary initial values. The application of the SIR model for the description of COVID-19 propagation dynamic is demonstrated. Springer US 2023-04-05 2022 /pmc/articles/PMC10074335/ http://dx.doi.org/10.1007/s10598-023-09572-7 Text en © Springer Science+Business Media, LLC, part of Springer Nature 2023, Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Semendyaeva, N. L.
Orlov, M. V.
Rui, Tang
Enping, Yang
Analytical and Numerical Investigation of the SIR Mathematical Model
title Analytical and Numerical Investigation of the SIR Mathematical Model
title_full Analytical and Numerical Investigation of the SIR Mathematical Model
title_fullStr Analytical and Numerical Investigation of the SIR Mathematical Model
title_full_unstemmed Analytical and Numerical Investigation of the SIR Mathematical Model
title_short Analytical and Numerical Investigation of the SIR Mathematical Model
title_sort analytical and numerical investigation of the sir mathematical model
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10074335/
http://dx.doi.org/10.1007/s10598-023-09572-7
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AT orlovmv analyticalandnumericalinvestigationofthesirmathematicalmodel
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AT enpingyang analyticalandnumericalinvestigationofthesirmathematicalmodel

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