Optimal Perturbations of Systems with Delayed Independent Variables for Control of Dynamics of Infectious Diseases Based on Multicomponent Actions

In this paper, we apply optimal perturbations to control mathematical models of infectious diseases expressed as systems of nonlinear differential equations with delayed independent variables. We develop the method for calculation of perturbations of the initial state of a dynamical system with dela...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 253; no. 5; pp. 618 - 641
Main Authors Bocharov, G. A., Nechepurenko, Yu. M., Khristichenko, M. Yu, Grebennikov, D. S.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2021
Springer
Springer Nature B.V
Subjects
Analysis
Control
Differential equations
Health aspects
Independent variables
Infectious diseases
Mathematical models
Mathematics
Mathematics and Statistics
Nonlinear differential equations
Nonlinear systems
Perturbation
Virus diseases
Viruses
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Summary:In this paper, we apply optimal perturbations to control mathematical models of infectious diseases expressed as systems of nonlinear differential equations with delayed independent variables. We develop the method for calculation of perturbations of the initial state of a dynamical system with delayed independent variable producing maximal amplification in the given local norm taking into account weights of perturbation components. For the model of experimental virus infection, we construct optimal perturbation for two types of stationary states, with low or high viral load, corresponding to different variants of chronic virus infection flow.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05258-w