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I am working on a model of aggregation behavior modeled with the Keller-Segel PDE system. I recently gave a talk on this and was asked what other examples there were of the Keller-Segel system. Since this is an obvious question, I was embarrassed to have no example other than my model and the aggregation of cellular slime molds (the application for which the Keller-Segel model was originally devloped). So I did some googling and came up with bupkis. There are hundreds of papers about the system by mathematicians, but I failed to find any other biological examples.

What about it? Is the Keller-Segel model mostly just a mathematical curiosity, or is it a model with many real applications to biology?

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This looks like a good starting place: Painter, K. J. “Mathematical Models for Chemotaxis and Their Applications in Self-Organisation Phenomena,” June 22, 2018. https://arxiv.org/abs/1806.08627v2 (published in Journal of Theoretical Biology, 2019). Lists examples from Dictyostelium (of course), bacterial aggregation, development, physiology and disease, ecology, social science.

In this review, I evaluate the use of PKS [Patlak-Keller-Segel] models in describing chemotaxis (and other taxes), particularly focussing on examples of pattern formation/self-organisation. I do not review the numerous excellent studies that primarily concentrate on their mathematical analysis: a number of reviews already cover these aspects in depth [...] Next, the fundamental modelling that led to (1) is reviewed and an overview given regarding its patterning behaviour. I then proceed field-by-field, beginning with its motivations in microbiology and sweeping across areas including developmental biology, immunology, cancer, ecology and the social sciences. For each case, the historical justification for chemotaxis is described and models are discussed; a compendium that contains many of these models is provided in the Appendix. Finally, I demonstrate how PKS models can continue to penetrate new areas, via a novel application to explain clique formation in research.

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