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 (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.
Keywords
Tumour-Immune interactions
Phenotype-structured model
Asymptotic analysis
Immune checkpoint inhibitors
Tumour-Immune interactions Phenotype-structured model Asymptotic analysis Immune checkpoint inhibitors. 2020 MSC: 35B40 35F50 35Q92 92-10 92C50 92D25
Tumour-Immune interactions
Immune checkpoint inhibitors. 2020 MSC: 35B40
35F50
35Q92
92-10
92C50
92D25
Domains
Analysis of PDEs [math.AP]
Origin : Files produced by the author(s)