Abstract
Keller-Segel equations are widely employed to explain chemotaxis-induced bacterial traveling band phenomena. In this system, the dispersal of bacteria is modeled by independently given diffusion and advection terms, and the growth of cell population is neglected. In the paper, we develop a chemotaxis model which consists of cross-diffusion and population growth. In particular, we consider the case that the diffusion and advection terms form an exact cross-diffusion. The developed mathematical models are based on the conversion dynamics between active and inactive cells with different dispersal rates. The process consists of three steps and the performance of each step is complemented by comparing numerical simulations and experimental data.
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