# Optimal Control for a Mathematical Model of Glioma Treatment with Oncolytic Therapy and TNF- $$\alpha$$ α Inhibitors

Optimal Control for a Mathematical Model of Glioma Treatment with Oncolytic Therapy and TNF-... A mathematical model for combination therapy of glioma with oncolytic therapy and TNF- $$\alpha$$ α inhibitors is analyzed as an optimal control problem. In the objective, a weighted average between the tumor volume and the total amount of viruses given is minimized. It is shown that optimal controls representing the virus administration are generically of the bang-bang type, i.e., the virus should be applied at maximal allowed dose with possible rest periods. On the other hand, optimal controls representing the dosage of TNF- $$\alpha$$ α inhibitors follow a continuous regimen of concatenations between pieces that lie on the boundary and in the interior of the control set. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Optimization Theory and Applications Springer Journals

# Optimal Control for a Mathematical Model of Glioma Treatment with Oncolytic Therapy and TNF- $$\alpha$$ α Inhibitors

, Volume 176 (2) – Jan 18, 2018
22 pages

/lp/springer_journal/optimal-control-for-a-mathematical-model-of-glioma-treatment-with-WM8rTiny4F
Publisher
Springer Journals
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory
ISSN
0022-3239
eISSN
1573-2878
D.O.I.
10.1007/s10957-018-1218-4
Publisher site
See Article on Publisher Site

### Abstract

A mathematical model for combination therapy of glioma with oncolytic therapy and TNF- $$\alpha$$ α inhibitors is analyzed as an optimal control problem. In the objective, a weighted average between the tumor volume and the total amount of viruses given is minimized. It is shown that optimal controls representing the virus administration are generically of the bang-bang type, i.e., the virus should be applied at maximal allowed dose with possible rest periods. On the other hand, optimal controls representing the dosage of TNF- $$\alpha$$ α inhibitors follow a continuous regimen of concatenations between pieces that lie on the boundary and in the interior of the control set.

### Journal

Journal of Optimization Theory and ApplicationsSpringer Journals

Published: Jan 18, 2018

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