Competition of motile and immotile bacterial strains in a petri dish

Bacterial competition is an important component in many practicalapplications such as plant roots colonization and medicine(especially in dental plaque). Bacterial motility has two types ofmechanisms --- directed movement (chemotaxis) and undirectedmovement. We study undirected bacterial movement mathematically andnumerically which is rarely considered in literature. To studybacterial competition in a petri dish, we modify and extend themodel used in Wei et al. (2011) to obtain a group of more generaland realistic PDE models. We explicitly consider the nutrients andincorporate two bacterial strains characterized by motility. We usedifferent nutrient media such as agar and liquid in the theoreticalframework to discuss the results of competition. The consistency ofour numerical simulations and experimental data suggest theimportance of modeling undirected motility in bacteria. In agar themotile strain has a higher total density than the immotile strain,while in liquid both strains have similar total densities.Furthermore, we find that in agar as bacterial motility increases,the extinction time of the motile bacteria decreases withoutcompetition but increases in competition. In addition, we show theexistence of traveling-wave solutions mathematically andnumerically.