Linking Self-Organization of Bacterial and Human Populations in Mathematical Models of Chemotaxis

This paper analyses the self-organization and spatio-temporal pattern formation in bacterial and human populations using chemotaxis-based mathematical models. The pattern formation in the following three chemotaxis-type systems is investigated: the self-organization of suspensions of luminous Escherichia coli bacteria, the capital-induced labor migration in a spatial Solow model, and the movement of urban criminals forming crime hotspots. The three models are selected as representative examples of chemotaxis mechanisms that capture distinct modeling assumptions and applications. Nonlinear two-dimensional as well as one-dimensional-in-space reaction–diffusion–chemotaxis models were used to simulate the pattern formation in all three chemotactic systems within a restricted area—a circle. The models are formulated in dimensionless form, and the corresponding dimensional parameters are estimated through the comparison of simulation results with experimental and statistical data. The numerical simulation under the transient conditions was carried out using the finite difference technique. This study highlights substantial differences between bacterial motility and the geographical movement of humans; however, human populations’ movement toward an attractant can be regarded as analogous to the chemotactic behavior of biological cells, differing primarily in scale.