A mathematical model of cytotoxic and helper T cell interactions in a tumour microenvironment

Abstract We develop a mathematical model to examine the role of helper and cytotoxic T cells in an anti-tumour immune response. The model comprises three ordinary differential equations describing the dynamics of the tumour cells, the helper and the cytotoxic T cells, and implicitly accounts for immunosuppressive effects. The aim is to investigate how the anti-tumour immune response varies with the level of infiltrating helper and cytotoxic T cells. Through a combination of analytical studies and numerical simulations, our model exemplifies the three Es of immunoediting: elimination, equilibrium and escape. Specifically, it reveals that the three Es of immunoediting depend highly on the infiltration rates of the helper and cytotoxic T cells. The model’s results indicate that both the helper and cytotoxic T cells play a key role in tumour elimination. They also show that combination therapies that boost the immune system and block tumour-induced immunosuppression may have a synergistic effect in reducing tumour growth.