Competition of motile and immotile bacterial strains in a petri dish

Bacterial competition is an important component in many practical applications such as plant roots colonization and medicine (especially in dental plaque). Bacterial motility has two types of mechanisms -- directed movement (chemotaxis) and undirected movement. We study undirected bacterial movement mathematically and numerically which is rarely considered in literature. To study bacterial competition in a petri dish, we modify and extend the model used in Wei et al. (2011) to obtain a group of more general and realistic PDE models. We explicitly consider the nutrients and incorporate two bacterial strains characterized by motility. We use different nutrient media such as agar and liquid in the theoretical framework to discuss the results of competition. The consistency of our numerical simulations and experimental data suggest the importance of modeling undirected motility in bacteria. In agar the motile strain has a higher total density than the immotile strain, while in liquid both strains have similar total densities. Furthermore, we nd that in agar as bacterial motility increases, the extinction time of the motile bacteria decreases without competition but increases in competition. In addition, we show the existence of traveling-wave solutions mathematically and numerically.