Traveling wave solutions of a reaction–diffusion model for bacterial growth

In this paper, we consider a reaction–diffusion model for the bacterial growth. Mathematical analysis on the traveling wave solutions of the model is performed. This includes traveling wave analysis and numerical simulations of wave front propagation for a special case. Specifically, we show that such solutions exist only for wave speeds greater than some minimum speed giving wave with a sharp front. The minimum speed is estimated and the wave profile is calculated and compared with different numerical methods.