A phenotype-structured model for the tumour-immune response

TL;DR

This paper introduces a mathematical model capturing tumour-immune interactions with cell heterogeneity, analyzing immune response dynamics and the effects of immune checkpoint inhibitors through theoretical and numerical methods.

Contribution

It develops a novel phenotype-structured integro-differential model for tumour-immune dynamics, including the impact of immunotherapy, and provides asymptotic analysis and simulations.

Findings

Model reproduces the three Es of immunoediting: elimination, equilibrium, escape.

Asymptotic behavior characterized under convergence hypotheses.

Simulations show impact of ICIs on tumour-immune interaction states.

Abstract

This paper presents a mathematical model for tumour-immune response interactions in the perspective of immunotherapy by immune checkpoint inhibitors ICIs. The model is of the nonlocal integro-differential Lotka-Volterra type, in which heterogeneity of the cell populations is taken into account by structuring variables that are continuous internal traits (aka phenotypes) present in each individual cell. These represent a lumped ``aggressiveness'', i.e., for tumour cells, malignancy understood as the ability to thrive in a viable state under attack by immune cells or drugs - which we propose to identify as a potential of de-differentiation -, and for immune cells, ability to kill tumour cells, in other words anti-tumour efficacy. We analyse the asymptotic behaviour of the model in the absence of treatment. By means of two theorems, we characterise the limits of the integro-differential system under an a priori convergence hypothesis. We illustrate our results with a few numerical simulations, which show that our model reproduces the three Es of immunoediting: elimination, equilibrium, and escape. Finally, we exemplify the possible impact of ICIs on these three Es.