Traveling Wavefronts in a Volume-Filling Chemotaxis Model

Chemotaxis is an observed phenomenon in which an organism moves preferentially toward a relatively high concentration, which is contrary to the process of natural diffusion. In this paper, we study a volume-filling model of chemotaxis and provide a valid approach to establishing the existence of traveling wavefronts via the Banach fixed point theorem. Rigorous results hold either when the chemotactic sensitivity is relatively small or when the wave speed is large. Numerical simulations are presented to illustrate the main results, and comparisons of wave patterns in different parameters are demonstrated.