We provide a review of recent advancements in non-local continuous models for migration,
mainly from the perspective of its involvement in embryonal development and cancer …

The employment of nonlocal PDE models to describe biological aggregation and other
phenomena has gained considerable traction in recent years. For cell populations, these …

Abstract Transforming growth factor-\(\beta\)(TGF-\(\beta\)) is a crucial regulator of fibroblast
cell function and is essential for maintaining and repairing connective tissues in the body …

Recognised as one of the hallmarks of cancer, local cancer cell invasion is a complex
multiscale process that combines the secretion of matrix-degrading enzymes with a series of …

The transition from the epithelial to mesenchymal phenotype and its reverse (from
mesenchymal to epithelial) are crucial processes necessary for the progression and spread …

Quantitative modelling is increasingly important in cancer research, hel** to integrate
myriad diverse experimental data into coherent pictures of the disease and able to …

Cells adhere to each other and to the extracellular matrix (ECM) through protein molecules
on the surface of the cells. The breaking and forming of adhesive bonds, a process critical in …

The movement of cells in spatial micro-environments can be modeled by continuous
variables for the continuum density of the cells. The partial differential equations of these …

Local cancer invasion of tissue is a complex, multiscale process which plays an essential
role in tumour progression. During the complex interaction between cancer cell population …

In 2006 Armstrong, Painter, and Sherratt formulated a nonlocal differential equation model
for cell-cell adhesion. For the one-dimensional case on a bounded domain we derive …