Geodesic
On solving the optimization problem for chemotherapy process in terms of the maximum principle
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2012), pp. 63-67.

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We consider the problems of optimal control for chemotherapy process based on a well-known dynamic model. The solution method is related to combining the control modes that appear according to the Pontryagin maximum principle. We construct extreme procedures of control with special sections that amplify the known strategies of therapy within the given model.
Keywords: optimal control problem, maximum principle, extremal processes. 
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     title = {On solving the optimization problem for chemotherapy process in terms of the maximum principle},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {63--67},
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}
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V. A. Srochko. On solving the optimization problem for chemotherapy process in terms of the maximum principle. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2012), pp. 63-67. http://geodesic.mathdoc.fr/item/IVM_2012_7_a8/

[1] Antipov A. V., Bratus A. S., “Matematicheskaya model optimalnoi strategii khimioterapii s uchetom dinamiki chisla kletok neodnorodnoi opukholi”, Zhurn. vychisl. matem. i matem. fiz., 49:11 (2009), 1907–1919 | MR | Zbl

[2] Aranjo R. P., Mcelwain D. L., “A history of the study of solid tumour growth: the contribution of mathematical modeling”, Bull. Math. Biol., 66:5 (2004), 1039–1091 | DOI | MR

[3] Costa M. S., Boldrini J. L., Bassanezi R. C., “Drug kinetics and drug resistance in optimal chemotherapy”, Math. Biosciences, 125:2 (1995), 191–209 | DOI | Zbl

[4] Arguchintsev A. V., Dykhta V. A., Srochko V. A., “Optimalnoe upravlenie: nelokalnye usloviya, vychislitelnye metody i variatsionnyi printsip maksimuma”, Izv. vuzov. Matem., 2009, no. 1, 3–43 | MR | Zbl