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

  • Heidi Dritschel Mathematical Institute, University of Oxford, Oxford, UK
  • Sarah L. Waters Mathematical Institute, University of Oxford, Oxford, UK
  • Andreas Roller Roche Pharmaceutical Research and Early Development, Roche Innovation Center Basel, Basel, Switzerland https://orcid.org/0000-0001-6335-0962
  • Helen M. Byrne Mathematical Institute, University of Oxford, Oxford, UK https://orcid.org/0000-0003-1771-5910
Keywords: Cancer, immunology, Tcells, ODEs, asymptotics

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.

Published
2018-06-30
How to Cite
Dritschel, Heidi, Sarah Waters, Andreas Roller, and Helen Byrne. 2018. “A Mathematical Model of Cytotoxic and Helper T Cell Interactions in a Tumour Microenvironment”. Letters in Biomathematics 5 (2), S36–S68. https://doi.org/10.1080/23737867.2018.1465863.
Section
Research