Dynamics of tumor-immune interaction under treatment as an optimal control problem

Urszula Ledzewicz; Mohammad Naghnaeian; Heinz Schättler

doi:10.3934/proc.2011.2011.971

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2011, Volume 2011: 971-980. Doi: 10.3934/proc.2011.2011.971 open access

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Dynamics of tumor-immune interaction under treatment as an optimal control problem

1.
Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL 62026
2.
Dept. of Mechanical Science and Engineering, Univeristy of Illinois at Urbana-Champaign, 1206 W. Green Street, Urbana, IL, 61801-2906
3.
Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, 63130-4899

Received: June 30, 2010

Revised: July 31, 2010

Published: August 2017

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Abstract

For a mathematical model for cancer-immune system interactions under chemotherapy, we consider the problem of moving an initial condition that lies in a region of malignant cancer growth through therapy into a region where cancer regresses and thus control the cancer. We formulate this treatment goal as an optimal control problem and discuss the solutions for various related objective functions in the model.

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Mathematics Subject Classification: Primary: 49K15; Secondary: 92C50.

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