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Optimal Control with an Isoperimetric Constraint Applied to Cancer Immunotherapy

by Amine Hamdache, Ilias Elmouki, Smahane Saadi
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 94 - Number 15
Year of Publication: 2014
Authors: Amine Hamdache, Ilias Elmouki, Smahane Saadi
10.5120/16421-6073

Amine Hamdache, Ilias Elmouki, Smahane Saadi . Optimal Control with an Isoperimetric Constraint Applied to Cancer Immunotherapy. International Journal of Computer Applications. 94, 15 ( May 2014), 31-37. DOI=10.5120/16421-6073

@article{ 10.5120/16421-6073,
author = { Amine Hamdache, Ilias Elmouki, Smahane Saadi },
title = { Optimal Control with an Isoperimetric Constraint Applied to Cancer Immunotherapy },
journal = { International Journal of Computer Applications },
issue_date = { May 2014 },
volume = { 94 },
number = { 15 },
month = { May },
year = { 2014 },
issn = { 0975-8887 },
pages = { 31-37 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume94/number15/16421-6073/ },
doi = { 10.5120/16421-6073 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:17:46.264307+05:30
%A Amine Hamdache
%A Ilias Elmouki
%A Smahane Saadi
%T Optimal Control with an Isoperimetric Constraint Applied to Cancer Immunotherapy
%J International Journal of Computer Applications
%@ 0975-8887
%V 94
%N 15
%P 31-37
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, a therapeutic strategy for the treatment of cancer using immunotherapy that aims to maximize the active immune response and to minimize the tumor cells level while reducing drugs side effects and treatment cost is proposed. Assume that the treatment amount that can be administered to a potential patient during therapy period is known precisely, an ODE model with control acting as an immunotherapy agent is presented and an optimal control problem is formulated to include an isoperimetric constraint on the immunotherapy treatment. The Pontryagin's maximum principle is used to characterize the optimal control taking into account the fixed isoperimetric constraint. The optimality system is derived and solved numerically using an adapted iterative method with a Runge-Kutta fourth order scheme and secant method routine.

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Index Terms

Computer Science
Information Sciences

Keywords

Interleukin-2 Isoperimetric constraint Pontryagin's maximum principle Runge-Kutta fourth order scheme Secant method routine

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