Journal of Mathematical Sciences

, Volume 230, Issue 5, pp 762–765

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

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

## 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

49J99 92C99

## 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