The goal of this talk is to study a fourth-order nonlinear parabolic system with dispersion for describing bacterial aggregation. It shows that unlike the model without dispersion, a bacterial cluster can move, which allows us to consider dispersion as some kind of control for bacterial colony. Analytical solution of traveling wave is found by taking into account the dispersion coefficient. Numerically, we demonstrate that the initial concentration of bacteria in the form of a random distribution over time transforms into a periodic wave, followed by a transitionto a stationary solitary wave without dispersion.