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JOURNALS // Trudy Instituta Matematiki i Mekhaniki UrO RAN // Archive

Trudy Inst. Mat. i Mekh. UrO RAN, 2020 Volume 26, Number 1, Pages 173–181 (Mi timm1708)

Construction of the viability set in a problem of chemotherapy of a malignant tumor growing according to the Gompertz law

N. G. Novoselovaab, N. N. Subbotinaab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

Abstract: The problem of chemotherapy of a malignant tumor growing according to the Gompertz law is considered. The mathematical model is a system of two ordinary differential equations. We study a problem of optimal control (optimal therapy) aiming at the minimization of the malignant cells in the body at a given terminal time $T$. The viability set of this problem, i.e., the set of initial states of the model (the volume of the tumor and the amount of the drug in the body) for which an optimal control guarantees that the dynamics of the system up to the time $T$ is compatible with life in terms of the volume of the tumor, is constructed analytically.

Keywords: viability set, optimal control, value function.

UDC: 517.977

MSC: 49L25, 49K15, 65K05

Received: 15.10.2019
Revised: 17.01.2020
Accepted: 20.01.2020

DOI: 10.21538/0134-4889-2020-26-1-173-181



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