Existence of travelling waves in a spatial model of bacteria quiescence

Abstract

This work presents a reaction–diffusion model that captures the spatio-temporal evolution of a bacterial colony and takes into account the quiescent stage. Using the theory of monotone wavefronts for cooperative and partially degenerate reaction–diffusion systems, we establish the existence of travelling waves and show that the spreading speed coincides with the minimal wave speed. Furthermore, we show the existence of travelling waves using the method of constructing a pair of upper and lower solutions for a non-cooperative partially degenerate differential system of equations. Results demonstrate that neglecting dormant cell dynamics overestimates the spreading speed of the colony. Numerical simulations are provided to illustrate our results.