A population dynamics model of cell-cell adhesion incorporating population pressure and density saturation

•An improved continuum model for cell-cell adhesion is proposed.•Model based on two basic principles: total population pressure and force saturation response.•Excellent agreement with experimental data by Katsunuma et al.•Model sensitivity on the potential shape and cell-cell repulsion. We discuss several continuum cell-cell adhesion models based on the underlying microscopic assumptions. We propose an improvement on these models leading to sharp fronts and intermingling invasion fronts between different cell type populations. The model is based on basic principles of localized repulsion and nonlocal attraction due to adhesion forces at the microscopic level. The new model is able to capture both qualitatively and quantitatively experiments by Katsunuma et al. (2016). We also review some of the applications of these models in other areas of tissue growth in developmental biology. We finally explore the resulting qualitative behavior due to cell-cell repulsion.