Reaction–Diffusion Model of CAR-T Cell Therapy in Solid Tumours with Antigen Escape

Developing effective CAR-T cell therapy for solid tumours remains challenging because of biological barriers such as antigen escape and an immunosuppressive microenvironment. The aim of this study is to develop a mathematical model of the spatio-temporal dynamics of tumour processes in order to assess key factors that limit treatment efficacy. We propose a reaction–diffusion model described by a system of partial differential equations for the densities of tumour cells and CAR-T cells, the concentration of immune inhibitors, and the degree of antigen escape. The methods of investigation include stability analysis and numerical solution of the model using a finite-difference scheme. The simulation results show that antigen escape leads to the formation of a persistent core within the tumour and subsequent relapse after an initial regression. We find that the efficacy of therapy critically depends on the balance between the rate of tumour-cell killing and the rate of resistance development, and that repeated administration of CAR-T cells provides deeper and more durable suppression of tumour growth compared with a single infusion. We conclude that the proposed model is a valuable tool for analysing and optimising CAR-T therapy protocols, and that our results highlight the need for combined strategies aimed at overcoming antigen escape.