Journal
JOURNAL OF BIOLOGICAL SYSTEMS
Volume 27, Issue 2, Pages 225-255Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218339019500104
Keywords
Brain Tumor; T11 Target Structure (T11TS); Optimal Control
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Funding
- Science and Engineering Research Board [ECR/2017/000234]
- Department of Science and Technology, Government of India
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We report a mathematical model depicting gliomas and immune system interactions by considering the role of immunotherapeutic drug T11 target structure (T11TS). The mathematical model comprises a system of coupled nonlinear ordinary differential equations involving glioma cells, macrophages, activated cytotoxic T-Iymphocytes (CTLs), immunosuppressive cytokine transforming growth factor-beta (TGF-beta), immunostimulatory cytokine interferon-gamma (IFN-gamma) and the concentrations of immunotherapeutic agent T11TS. For the better understanding of the circumstances under which the gliomas can be eradicated from a patient, we use optimal control strategy. We design the objective functional by considering the biomedical goal, which minimizes the glioma burden and maximizes the macrophages and activated CTLs. The existence and the characterization for the optimal control are established. The uniqueness of the quadratic optimal control problem is also analyzed. We demonstrate numerically that the optimal treatment strategies using T11TS reduce the glioma burden and increase the cell count of activated CTLs and macrophages.
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