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Preprints, Working Papers, ... Year : 2023

A phenotype-structured model for the tumour-immune response


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.
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Dates and versions

hal-03936993 , version 1 (13-01-2023)
hal-03936993 , version 2 (13-03-2023)
hal-03936993 , version 3 (29-08-2023)



Zineb Kaid, Camille Pouchol, Jean Clairambault. A phenotype-structured model for the tumour-immune response. 2023. ⟨hal-03936993v3⟩
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