Belmonte Beitia, Juan. Italia, Matteo. 

Malignant gliomas (MGs) are among the most aggressive primary brain tumors, characterized by a high degree of resistance to therapy and poor prognosis. In this work, we develop a mathematical model to investigate the dynamics of MG under the combined effects of chemotherapy and chimeric antigen receptor cell therapy. The proposed model is a five-dimensional dynamical system incorporating impulsive inputs that correspond to the clinical administration of chemotherapy and immunotherapy. We demonstrate the non-negativity of solutions for non-negative initial conditions, ensuring the biological relevance of the model. We show that if we apply both therapies only once, the trajectories are attracted to an invariant surface corresponding to the tumor carrying capacity. Conversely, under constant administration of both treatments, we identify parameter ranges in which tumor eradication is achievable. Furthermore, we numerically study various treatment combinations to determine optimal protocols at the population level. To this end, we generate a cohort of virtual patients with model parameters sampled uniformly within clinically relevant ranges and carry out in silico trials. Our findings indicate that tumor growth rate, chemotherapy efficacy, and tumor-induced immunosuppression are the key determinants of survival outcomes. We believe that our results provide new theoretical insights into treatment optimization and offer a framework for refining the design of clinical trials for MG therapies.