A phenotype-structured model for the tumour-immune response

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 integrodifferential Lotka-Volterra type, in which heterogeneity of the cell populations is taken into account by structuring variables that are continuous internal traits (aka phenotypes) representing a lumped ''aggressiveness'', i.e., for tumour cells, 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. 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 numerical simulations, which show that our model exemplifies the three Es of immunoediting: elimination, equilibrium, and escape