Understanding the mechanisms behind cell population dynamics is essential to a wide range of biological processes including development, wound healing, tumor expansion, and immune responses. The mathematical model system is applicable to many biological systems such as swarming microglia and neutrophils or accumulating ants towards a localized food source. We find that the cell-to-cell interaction confers a far more compact aggregation resulting in a much higher peak equilibrium cell density. In the absence of the cell-to-cell interaction, the equilibrium population density profile fits well to that of a simple Keller-Segal population dynamic model, in which a chemotactic current density competes with a normal diffusive current density, where p and ρ refer to the concentration of chemoattractant and population density, respectively. Here, we report an interesting aggregation dynamics of mathematical model cells, when they perform chemotaxis in response to an externally imposed global chemical gradient while they influence each other through a haptotaxis-mediated social interaction, which confers intriguing trail patterns. Some of these processes are intrinsic to individual cells, while others pertain to cell-to-cell interactions and to their responses to extrinsically imposed cues. The crawling of biological cell is a complex phenomenon involving various biochemical and mechanical processes.
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