Mathematical model of CAR-T therapy taking into account cells targeting off-tumour antigens

Abstract

In [1] two mathematical models of CAR-T (Chimeric Antigen Receptor T) cell therapy were presented. The results of this therapy against leukaemias and lymphomas were positive [2, 3], but in the case of solid tumours, including glioblastoma the results were less optimistic [4, 5]. We will focus on the mathematical analysis of one of presented models, that takes into account CAR-T cells targeting no-tumour and off-tumour antigens. The system consist of four ordinary differential equations. In [1] only an initial dose of CAR-T cell treatment was considered. We consider two kind of treatments: a constant one (which will be modelled by a source term of CAR-T cells) and periodic one (modelled by an impulsive differential equations). Basic mathematical properties of the model will be presented as well as an asymptotic dynamics of solutions will be discussed.