Non-local models for spatio-temporal macrophage-tumour co-invasion: role of competition for resources
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 M1 and M2 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.
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BibTeX
@article{marguet2026nonlocal,
title = {{Non-local models for spatio-temporal macrophage-tumour co-invasion: role of competition for resources}},
author = {Johan Marguet and Raluca Eftimie},
journal = {Applied Mathematics and Computation},
year = {2026},
month = sep,
doi = {10.1016/j.amc.2026.130317},
url = {https://hal.science/hal-05754494v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Non-local models for spatio-temporal macrophage-tumour co-invasion: role of competition for resources
AU - Johan Marguet
AU - Raluca Eftimie
PY - 2026
DA - 2026/09/22
JO - Applied Mathematics and Computation
DO - 10.1016/j.amc.2026.130317
UR - https://hal.science/hal-05754494v1
AB - 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 M1 and M2 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.
SN - 0096-3003
ER -