Tumour-immune dynamics with an immune checkpoint inhibitor

  • Elpiniki Nikolopoulou School of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ, USA
  • Lauren R. Johnson aSchool of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ, USA
  • Duane Harris aSchool of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ, USA
  • John D. Nagy School of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ, USA; Department of Biology, Scottsdale Community College, Scottsdale, AZ, USA
  • Edward C. Stites Integrative Biology Laboratory, Salk Institute for Biological Studies, La Jolla, CA, USA
  • Yang Kuang School of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ, USA
Keywords: Immunotherapy, mathematical oncology, checkpoint inhibitor, tumour, PD-1, PD-L1, anti-PD-1, tumour/immune model

Abstract

The use of immune checkpoint inhibitors is becoming more commonplace in clinical trials across the nation. Two important factors in the tumour-immune response are the checkpoint protein programmed death-1 (PD-1) and its ligand PD-L1. We propose a mathematical tumour-immune model using a system of ordinary differential equations to study dynamics with and without the use of anti-PD-1. A sensitivity analysis is conducted, and series of simulations are performed to investigate the effects of intermittent and continuous treatments on the tumour-immune dynamics. We consider the system without the anti-PD-1 drug to conduct a mathematical analysis to determine the stability of the tumour-free and tumorous equilibria. Through simulations, we found that a normally functioning immune system may control tumour. We observe treatment with anti-PD-1 alone may not be sufficient to eradicate tumour cells. Therefore, it may be beneficial to combine single agent treatments with additional therapies to obtain a better antitumour response.

Published
2018-06-30
How to Cite
Nikolopoulou, Elpiniki, Lauren Johnson, Duane Harris, John Nagy, Edward Stites, and Yang Kuang. 2018. “Tumour-Immune Dynamics With an Immune Checkpoint Inhibitor”. Letters in Biomathematics 5 (2), S137–S159. https://doi.org/10.1080/23737867.2018.1440978.
Section
Research