On the Analysis of a Mathematical Model of CAR–T Cell Therapy for Glioblastoma: Insights from a Mathematical Model

Chimeric antigen receptor T (CAR-T) cell therapy has been proven to be successful against different leukaemias and lym-phomas. Its success has led, in recent years, to its use being tested for different solid tumours, including glioblastoma,a type of primary brain tumour, characterised by aggressiveness and recurrence. This paper presents an analytical studyof a mathematical model describing the competition of CAR-T and glioblastoma tumour cells, taking into account theirimmunosuppressive capacity. The model is formulated in a general way, and its basic properties are investigated. However,most of the analysis considers the model with exponential tumour growth, assuming this growth type for simplicity. Theexistence and stability of steady states are studied, and the subsequent focus is on two different types of treatment: con-stant and periodic. Finally, protocols for CAR-T cell therapy of glioblastoma are numerically derived; these are aimed atpreventing the tumour from reaching a critical size and at prolonging the patients’ survival time as much as possible. Theanalytical and numerical results provide theoretical support for the treatment of glioblastoma using CAR-T cells.