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

Elzbieta Ratajczyk, Urszula Ledzewicz () and Heinz Schättler ()
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Elzbieta Ratajczyk: Lodz University of Technology
Urszula Ledzewicz: Lodz University of Technology
Heinz Schättler: Washington University

Journal of Optimization Theory and Applications, 2018, vol. 176, issue 2, No 10, 456-477

Abstract: 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.

Keywords: Optimal control; Oncolytic therapy; Singular control; High order necessary conditions for optimality; 49K15; 93C15 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-018-1218-4

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