The impact of immunotherapy on a glioma immune interaction model

Glioblastoma, a highly aggressive in primary brain tumor and has exceptionally poor prognosis, is refractory to conventional treatments, such as chemotherapy, surgery and radiation. This study aims at aiding in the design of more successful glioma therapy. To understand the dynamics under what circumstances the glioma cells can be eradicated, we propose and analyze a mechanistic model for malignant gliomas and immune system interplays that may ensue upon direct intra-tumoral administration of immunotherapeutic agent T11 target structure. Our mathematical model encompasses considerations of the interactive dynamics of glioma cells, glioma-specific CD8+T cells, macrophages, immuno-suppressive cytokine TGF-$\beta$ and immuno-stimulatory cytokine IFN-$\gamma$. The proposed mathematical model successfully retrieved clinical response to the immunotherapeutic drug T11 target structure for glioma cells. Our model enables us to identify the treatment regimen for a determined time window, in order to obtain an admissible concentration of glioma cell population. To mathematically model the dynamics of malignant gliomas development, before and after administration of immunotherapeutic treatment strategy, we derived the local asymptotic stability for the biologically feasible equilibrium points and the local relative controllability conditions for this coupled system of nonlinear ordinary differential equations. The system undergoes sensitivity analysis to identify the most sensitive parameters with respect to glioma cells. Numerical simulations were conducted for model verification and for retrieving putative treatment scenarios. The model simulations suggest that the immunotherapy has an impact in reducing the growth of glioma cell population and also an impact in enhancing the cell count of macrophages and CD8+T cell populations.