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

A mathematical model for combination therapy of glioma with oncolytic therapy and TNF-α<inline-graphic></inline-graphic> 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-α<inline-graphic></inline-graphic> inhibitors follow a continuous regimen of concatenations between pieces that lie on the boundary and in the interior of the control set. [ABSTRACT FROM AUTHOR]