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

Author

Listed:
  • Elzbieta Ratajczyk

    (Lodz University of Technology)

  • Urszula Ledzewicz

    (Lodz University of Technology
    Southern Illinois University Edwardsville)

  • Heinz Schättler

    (Washington University)

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.

Suggested Citation

  • Elzbieta Ratajczyk & Urszula Ledzewicz & Heinz Schättler, 2018. "Optimal Control for a Mathematical Model of Glioma Treatment with Oncolytic Therapy and TNF- $$\alpha $$ α Inhibitors," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 456-477, February.
    • Handle: RePEc:spr:joptap:v:176:y:2018:i:2:d:10.1007_s10957-018-1218-4
    DOI: 10.1007/s10957-018-1218-4
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    References listed on IDEAS

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    1. U. Ledzewicz & H. Schättler, 2002. "Optimal Bang-Bang Controls for a Two-Compartment Model in Cancer Chemotherapy," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 609-637, September.
    2. U. Ledzewicz & H. Schättler, 2012. "Multi-input Optimal Control Problems for Combined Tumor Anti-angiogenic and Radiotherapy Treatments," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 195-224, April.
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    Cited by:

    1. Elaiw, A.M. & Hobiny, A.D. & Al Agha, A.D., 2020. "Global dynamics of reaction-diffusion oncolytic M1 virotherapy with immune response," Applied Mathematics and Computation, Elsevier, vol. 367(C).

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