Modeling bacterial traveling wave patterns with exact cross-diffusion and population growth

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, growth cell population neglected. paper, we develop a chemotaxis model which consists cross-diffusion growth. particular, consider case that terms form an exact cross-diffusion. The developed mathematical models based on conversion dynamics between active inactive cells with different rates. process three steps performance each step complemented comparing numerical simulations experimental data.