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 of Optimization Theory and Applications – Springer Journals
Published: Jan 18, 2018
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