Work

Non-local models for spatio-temporal macrophage-tumour co-invasion: Role of competition for resources

Year: 2026

Type: article

Abstract: Competition for resources in the tumour microenvironment is known to drive cancer progression. In this study we propose a non-local mathematical model for macrophage-tumour interactions, and use it to investigate the role of M 1 and M 2 macrophages on tumour invasion into the surrounding tissue, and how this invasion is impacted by the competition for resources between cells. We show that the existence and stability of spatially homogeneous tumour-free and tumour-present steady states (where either there are no tumour cells, or there are tumour cells throughout the whole domain) depends on this implicit competition. Moreover, we show that the minimum speed at which the tumour invades the surrounding tissue (hence, the tumour aggressiveness) depends also on these resource competition coefficients. We conclude with an investigation of the spatial distribution of macrophages in various regions of the solid tumour, and emphasize the current lack of spatio-temporal data that could be used to gain further understanding of macrophages’ roles in tumour invasion.

Source: Applied Mathematics and Computation

DOI: 10.1016/j.amc.2026.130317

Authors: Johan Marguet, Raluca Eftimie

Institution: Laboratoire de Mathématiques de Besançon

Language: English

Topic: Mathematical Biology Tumor Growth

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,470

Funders: Agence Nationale de la Recherche, Conseil régional de Bourgogne-Franche-Comté