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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2025. Vol 54

Model of Control of the Economic System in Conditions of Mass Disease with Vaccination

Author(s)

Igor V. Lutoshkin1, Maria S. Rybina1

1 Ulyanovsk State University, Ulyanovsk, Russian Federation

Abstract
The paper proposes a mathematical model for optimal control of an economic entity in the context of a widespread disease outbreak. This model simultaneously reflects biological and socio-economic factors and is a modification of the model previously proposed by the authors, as it considers the factor of population vaccination. The resulting model is formulated as an optimal control problem with a pointwise delay in both the state and control variables. The model also includes intermediate constraints. To analyze the presented model, the Pontryagin function is applied, which allows conclusions to be drawn about the structure of the optimal control. The parameterization method is proposed to solve the obtained optimal control problem. The results of computational experiments with the proposed model are presented for the case when the model parameters are estimated using data on COVID-19 for 2020 in the Russian Federation.
About the Authors

Igor V. Lutoshkin, Cand. Sci. (Phys.Math.), Assoc. Prof., Ulyanovsk State University, Ulyanovsk, 43017, Russian Federation, lutoshkiniv@ulsu.ru

Maria S. Rybina, Ulyanovsk State University, Ulyanovsk, 432017, Russian Federation, rybina maria@icloud.com

For citation
Lutoshkin I. V., Rybina M. S. Model of Control of the Economic System in Conditions of Mass Disease with Vaccination. The Bulletin of Irkutsk State University. Series Mathematics, 2025, vol. 54, pp. 33–47. (in Russian) https://doi.org/10.26516/1997-7670.2025.54.33
Keywords
optimal control, economic system, mass disease, vaccination
UDC
517.977.5, 519.863
MSC
49M99, 91B55
DOI
https://doi.org/10.26516/1997-7670.2025.54.33
References
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