| Abstract: |
| We propose a mathematical model portraying glioma and immune system interactions, considering the role of immunotherapeutic drug T11 target structure. The mathematical model comprises of a system of coupled nonlinear ordinary differential equations involving glioma cells, macrophages, activated cytotoxic T - lymphocytes (CTLs), immunosuppressive cytokine TGF-$\beta$ (Transforming growth factor - $\beta$), immunostimulatory cytokine interferon-$\gamma$ (IFN - $\gamma$) and the concentrations of immunotherapeutic agent T11 target structure. For the better understanding of the circumstances under which the gliomas can be eradicated, we use optimal control theory. We design the objective functional by considering the biomedical goal, which minimizes the glioma burden and maximize the macrophages and activated CTLs. The existence and the characterization for the optimal control is established. The uniqueness of the quadratic optimal control problem is also analyzed. We demonstrate numerically that the optimal treatment strategies using T11 target structure reduce the glioma burden and increase the cell count of activated CTLs and macrophages. |
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