Mathematical models for cancer treatment that include immunological activity are considered as an optimal control problem with an objective that is motivated by a separatrix of the uncontrolled system. For various growth models on the cancer cells the existence and optimality of singular controls is investigated. For a Gompertzian growth function a synthesis of controls that move the state into the region of attraction of a benign equilibrium point is developed.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am38-1-2,
author = {Urszula Ledzewicz and Mohammad Naghnaeian and Heinz Sch\"attler},
title = {An optimal control approach to cancer treatment under immunological activity},
journal = {Applicationes Mathematicae},
volume = {38},
year = {2011},
pages = {17-31},
zbl = {1215.49030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am38-1-2}
}
Urszula Ledzewicz; Mohammad Naghnaeian; Heinz Schättler. An optimal control approach to cancer treatment under immunological activity. Applicationes Mathematicae, Tome 38 (2011) pp. 17-31. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am38-1-2/