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

By Heidi Dritschel, Sarah L. Waters, Andreas Roller and Helen M. Byrne


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

Topics: Cancer, immunology, Tcells, ODEs, asymptotics, Biology (General), QH301-705.5, Mathematics, QA1-939
Publisher: Taylor & Francis Group
Year: 2018
DOI identifier: 10.1080/23737867.2018.1465863
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