Mathematical model of the spread of a pandemic like COVID-19
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A. G. Sergeev, A. Kh. Khachatryan and Kh. A. Khachatryan;
Translated by: Christopher Hollings - Trans. Moscow Math. Soc. 2022, 55-65
- DOI: https://doi.org/10.1090/mosc/334
- Published electronically: September 23, 2024
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Abstract:
Using the example of the infectious disease called COVID-19, a mathematical model of the spread of a pandemic is considered. The virus that causes this disease emerged at the end of 2019 and spread to most countries around the world over the next year. A mathematical model of the emerging pandemic, called the SEIR-model (from the English words susceptible, exposed, infected, recovered), is described by a system of four ordinary dynamical equations given in §1.
The indicated system is reduced to a nonlinear integral equation of Hammerstein–Volterra type with an operator that does not have the property of monotonicity. In §3, we prove a theorem on the existence and uniqueness of a non-negative, bounded and summable solution of this system.
Based on real data on the COVID-19 disease in France and Italy, given in §2, numerical calculations are performed showing the absence of a second wave for the obtained solution.
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Bibliographic Information
- A. G. Sergeev
- Affiliation: Steklov Mathematical Institute of the Russian Academy of Sciences
- Email: sergeev@mi-ras.ru
- A. Kh. Khachatryan
- Affiliation: Armenian National Agrarian University, Yerevan
- Email: aghavard59@mail.ru
- Kh. A. Khachatryan
- Affiliation: Yerevan State University, Institute of Mathematics of the National Academy of Sciences of Armenia, Yerevan
- Email: khachatur.khachatryan@ysu.am, Khach82@rambler.ru
- Published electronically: September 23, 2024
- Additional Notes: In preparing this article, the first author received financial support from the Russian Science Foundation grant 19-11-00316 and the Russian Foundation for Basic Research grant 18-51-05009. The research of the second and third authors was carried out with the financial support of the RA Science Committee within the framework of the scientific project No. 21T-1A047. Sections 1 and 2 were written by A. G. Sergeev, the results of Section 3 belong to Kh. A. Khachatryan, and Section 4 to A. Kh. Khachatryan.
- © Copyright 2024 American Mathematical Society
- Journal: Trans. Moscow Math. Soc. 2022, 55-65
- MSC (2020): Primary 45G05, 92D30
- DOI: https://doi.org/10.1090/mosc/334