  The effect of mechanical interactions between cells in the spreading of
bacterial populations was investigated in one-dimensional space. A
continuum-mechanics approach, comprising cell migration, proliferation, and
exclusion processes, was employed to elucidate the dynamics. The consequent
nonlinear reaction-diffusion-like equation describes the constitution dynamics
of a bacterial population. In this model, bacterial cells were treated as
rod-like particles that interact with each other through hard-core repulsion,
which introduces the exclusion effect that causes bacterial populations to
migrate quickly and at high density. The propagation of bacterial density as a
traveling wave front over extended times was also analysed. The analytical and
numerical solutions revealed that the front speed was enhanced by the exclusion
process, which depended upon the cell-packing fraction. Finally, we
qualitatively compared our theoretical results with experimental evidence.
