Optimal Control for a Mathematical Model of Glioma Treatment with Oncolytic Therapy and TNF-$$\alpha $$ Inhibitors |
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| Authors: | Elzbieta Ratajczyk Urszula Ledzewicz Heinz Schättler |
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| Institution: | 1.Institute of Mathematics,Lodz University of Technology,Lodz,Poland;2.Department of Mathematics and Statistics,Southern Illinois University Edwardsville,Edwardsville,USA;3.Department of Electrical and Systems Engineering,Washington University,St. Louis,USA |
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| Abstract: | A mathematical model for combination therapy of glioma with oncolytic therapy and TNF-\(\alpha \) 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-\(\alpha \) inhibitors follow a continuous regimen of concatenations between pieces that lie on the boundary and in the interior of the control set. |
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