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Synthesis of optimal control in a mathematical model of tumour–immune dynamics
Author(s) -
Yegorov I.,
Todorov Y.
Publication year - 2013
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2103
Subject(s) - immune system , optimal control , dynamics (music) , mathematics , control theory (sociology) , chemotherapy , control (management) , computer science , mathematical optimization , immunology , biology , medicine , physics , surgery , artificial intelligence , acoustics
Summary An optimal control problem for a mathematical model of tumour–immune dynamics under the influence of chemotherapy is considered. The toxicity effect of the chemotherapeutic agent on both tumour and immunocompetent cells is taken into account. A standard linear pharmacokinetic equation for the chemotherapeutic agent is added to the system. The aim is to find an optimal strategy of treatment to minimize the tumour volume while keeping the immune response not lower than a fixed permissible level as far as possible. Sufficient conditions for the existence of not more than one switching and not more than two switchings without singular regimes are obtained. The surfaces in the extended phase space, on which the last switching appears, are constructed analytically.Copyright © 2013 John Wiley & Sons, Ltd.