Discrete Control of a Dynamical System with Delay Under Conditions of Uncertainty

In this paper, we present a numerical solution of the discrete control problem for the immune response in an infectious disease under conditions of uncertainty. This problem is described by a nonlinear system of ordinary differential equation with delay. Conditions of uncertainty mean that values of...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2018-05, Vol.230 (5), p.762-765
Main Authors: Rusakov, S. V., Chirkov, M. V.
Format: Article
Language:English
Subjects:
60 APPLIED LIFE SCIENCES
ALGORITHMS
CONTROL
Delay
DIFFERENTIAL EQUATIONS
Disease control
DYNAMICAL SYSTEMS
EXPERIMENTAL DATA
Immune system
IMMUNOTHERAPY
INFECTIOUS DISEASES
MATHEMATICAL METHODS AND COMPUTING
MATHEMATICAL MODELS
Mathematics
Mathematics and Statistics
NONLINEAR PROBLEMS
Nonlinear systems
NUMERICAL SOLUTION
Ordinary differential equations
Parameter identification
Parameter uncertainty
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Summary:In this paper, we present a numerical solution of the discrete control problem for the immune response in an infectious disease under conditions of uncertainty. This problem is described by a nonlinear system of ordinary differential equation with delay. Conditions of uncertainty mean that values of the parameters of the model are unknown and their estimates are corrected by new experimental data. We propose an algorithm that allows one, within the framework of the mathematical model of an infectious disease, to construct the control and to identify parameters. By using the algorithm proposed, we develop treatment programs based on immunotherapy. We show that immunotherapy is an effective treatment for all main forms of disease: acute, chronic, and lethal.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-018-3785-1