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

Abstract

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.

Authors:
;  [1]
  1. Perm State University (Russian Federation)
Publication Date:
OSTI Identifier:
22771271
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 230; Journal Issue: 5; Conference: International symposium on differential equations, Perm (Russian Federation), 17-18 May 2016; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; 60 APPLIED LIFE SCIENCES; ALGORITHMS; CONTROL; DIFFERENTIAL EQUATIONS; DYNAMICAL SYSTEMS; EXPERIMENTAL DATA; IMMUNOTHERAPY; INFECTIOUS DISEASES; MATHEMATICAL MODELS; NONLINEAR PROBLEMS; NUMERICAL SOLUTION

Citation Formats

Rusakov, S. V., E-mail: rusakov@psu.ru, and Chirkov, M. V., E-mail: rusakov@psu.ru. Discrete Control of a Dynamical System with Delay Under Conditions of Uncertainty. United States: N. p., 2018. Web. doi:10.1007/S10958-018-3785-1.
Rusakov, S. V., E-mail: rusakov@psu.ru, & Chirkov, M. V., E-mail: rusakov@psu.ru. Discrete Control of a Dynamical System with Delay Under Conditions of Uncertainty. United States. doi:10.1007/S10958-018-3785-1.
Rusakov, S. V., E-mail: rusakov@psu.ru, and Chirkov, M. V., E-mail: rusakov@psu.ru. Tue . "Discrete Control of a Dynamical System with Delay Under Conditions of Uncertainty". United States. doi:10.1007/S10958-018-3785-1.
@article{osti_22771271,
title = {Discrete Control of a Dynamical System with Delay Under Conditions of Uncertainty},
author = {Rusakov, S. V., E-mail: rusakov@psu.ru and Chirkov, M. V., E-mail: rusakov@psu.ru},
abstractNote = {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.},
doi = {10.1007/S10958-018-3785-1},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 5,
volume = 230,
place = {United States},
year = {2018},
month = {5}
}