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 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 (akaphenotypes) 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 ana prioriconvergence 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 ofICIs on these threeEs.