Geodesic
Discrete control of a dynamical system with delay under conditions of uncertainty
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Tome 132 (2017), pp. 109-112.

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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 the immunotherapy provides an effective treatment for all main forms of disease: acute, chronic, and lethal.
Keywords: mathematical model of an infectious disease, identification of parameters, discrete control, immunotherapy. 
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     author = {S. V. Rusakov and M. V. Chirkov},
     title = {Discrete control of a dynamical system with delay under conditions of uncertainty},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {109--112},
     publisher = {mathdoc},
     volume = {132},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_132_a24/}
}
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S. V. Rusakov; M. V. Chirkov. Discrete control of a dynamical system with delay under conditions of uncertainty. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Tome 132 (2017), pp. 109-112. http://geodesic.mathdoc.fr/item/INTO_2017_132_a24/