Dynamic systems and optimal control

Model of control of the economic system in conditions of mass disease with vaccination

I. V. Lutoshkin, M. S. Rybina

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.

Keywords: optimal control, economic system, mass disease, vaccination.

UDC: 517.977.5, 519.863

MSC: 49M99, 91B55

Received: 05.02.2025
Revised: 20.03.2025
Accepted: 15.04.2025

DOI: 10.26516/1997-7670.2025.54.33