Epidemic Waves and Exact Solutions of a Sequence of Nonlinear Differential Equations Connected to the SIR Model of Epidemics-Reference-Cited by-同舟云学术

Epidemic Waves and Exact Solutions of a Sequence of Nonlinear Differential Equations Connected to the SIR Model of Epidemics

Published:2023-03-01 Issue:3 Volume:25 Page:438
ISSN:1099-4300
Container-title:Entropy
language:en
Short-container-title:Entropy

Author:

Vitanov Nikolay K.¹²^ORCID,Vitanov Kaloyan N.¹

Affiliation:

1. Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria

2. Climate, Atmosphere and Water Research Institute, Bulgarian Academy of Sciences, Blvd. Tzarigradsko Chaussee 66, 1784 Sofia, Bulgaria

Abstract

The SIR model of epidemic spreading can be reduced to a nonlinear differential equation with an exponential nonlinearity. This differential equation can be approximated by a sequence of nonlinear differential equations with polynomial nonlinearities. The equations from the obtained sequence are treated by the Simple Equations Method (SEsM). This allows us to obtain exact solutions to some of these equations. We discuss several of these solutions. Some (but not all) of the obtained exact solutions can be used for the description of the evolution of epidemic waves. We discuss this connection. In addition, we use two of the obtained solutions to study the evolution of two of the COVID-19 epidemic waves in Bulgaria by a comparison of the solutions with the available data for the infected individuals.

Publisher

MDPI AG

Subject

General Physics and Astronomy

Link

https://www.mdpi.com/1099-4300/25/3/438/pdf

Reference87 articles.

1. Latora, V., Nicosia, V., and Russo, G. (2017). Complex Networks. Principles, Methods, and Applications, Cambridge University Press.

2. Chian, A.C.-L. (2007). Complex Systems Approach to Economic Dynamics, Springer.

3. Vitanov, N.K. (2016). Science Dynamics and Research Production. Indicators, Indexes, Statistical Laws and Mathematical Models, Springer.

4. Treiber, M., and Kesting, A. (2013). Traffic Flow Dynamics: Data, Models, and Simulation, Springer.

5. Manifesto for a Post-Pandemic Modeling;Kutner;Physica A,2019

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