Advertisement

Journal of Mathematical Sciences

, Volume 230, Issue 5, pp 762–765 | Cite as

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

  • S. V. Rusakov
  • M. V. Chirkov
Article
  • 14 Downloads

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.

Keywords and phrases

mathematical model of an infectious disease identification of parameters discrete control immunotherapy 

AMS Subject Classification

49J99 92C99 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    I. P. Bolodurina and Yu. P. Lugovskova, “Optimal control by the immune response,” Probl. Upravl., 5, 44–52 (2009).Google Scholar
  2. 2.
    G. I. Marchuk, Mathematical Modeling of Immune Response in Infectious Diseases, Springer-Verlag, Dordrecht (2013).Google Scholar
  3. 3.
    S. V. Rusakov and M. V. Chirkov, “Mathematical model of the influence of immunotherapy on the dynamics of the immune response,” Probl. Upravl., 6, 45–50 (2012).Google Scholar
  4. 4.
    S. V. Rusakov and M. V. Chirkov, “Identification of parameters and control in mathematical models of the immune response,” Ross. Zh. Biomekh., 18, No. 2, 259–269 (2014).Google Scholar
  5. 5.
    S. V. Rusakov and M. V. Chirkov, “On certain approaches to the mathematical modeling of the immune response in infectious diseases,” Vestn. Perm. Univ. Ser. Mat. Mekh. Inf. 1, No. 28, 45–55 (2015).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Perm State UniversityPermRussia

Personalised recommendations