Publication:
Analytical features of the SIR model and their applications to COVID-19

Файлы
W3088403292.pdf(1.13 MB)
Дата
2021
Авторы
Vigdorowitsch, M.
Kudryashov, N. A.
Chmykhov, M. A.
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Научные группы
Организационные подразделения
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Институт лазерных и плазменных технологий
Стратегическая цель Института ЛаПлаз – стать ведущей научной школой и ядром развития инноваций по лазерным, плазменным, радиационным и ускорительным технологиям, с уникальными образовательными программами, востребованными на российском и мировом рынке образовательных услуг.
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Аннотация
© 2020 Elsevier Inc.A classic two-parameter epidemiological SIR-model of the coronavirus propagation is considered. The first integrals of the system of non-linear equations are obtained. The Painlevé test shows that the system of equations is not integrable in the general case. However, the general solution is obtained in quadrature as an inverse time-function. Using the first integrals of the system of equations, analytical dependencies for the number of infected patients I(t) and that of recovered patients R(t) on the number of susceptible to infection S(t) are obtained. A particular attention is paid to interrelation of I(t) and R(t) both depending on α/β, where α is the contact rate in the community and β is the intensity of recovery/decease of patients. It is demonstrated that the data on particular morbidity waves in Hubei (China), Italy, Austria, South Korea, Moscow (Russia) as well some Australian territories are satisfactorily described by the expressions obtained for I(R). The variability of parameter N having been traditionally considered as a static population size is discussed.
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Цитирование
Vigdorowitsch, M. Analytical features of the SIR model and their applications to COVID-19 / Vigdorowitsch, M., Kudryashov, N.A., Chmykhov, M.A. // Applied Mathematical Modelling. - 2021. - 90. - P. 466-473. - 10.1016/j.apm.2020.08.057
URI
https://www.doi.org/10.1016/j.apm.2020.08.057
 https://www.scopus.com/record/display.uri?eid=2-s2.0-85091974707&origin=resultslist
 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:000590672100005
 https://openrepository.mephi.ru/handle/123456789/23445
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