It is well known that disinfection methods that successfully kill suspended bacterial populations often fail to eliminate bacterial biofilms. Recent efforts to understand biofilm survival have focused on the existence of small, but very tolerant, subsets of the bacterial population termed persisters. In this investigation, we analyze a mathematical model of disinfection that consists of a susceptible-persister population system embedded within a growing domain. This system is coupled to a reaction-diffusion system governing the antibiotic and nutrient.
We analyze the effect of periodic and continuous dosing protocols on persisters in a one-dimensional biofilm model, using both analytic and numerical method. We provide sufficient conditions for the existence of steady-state solutions and show that these solutions may not be unique. Our results also indicate that the dosing ratio (the ratio of dosing time to period) plays an important role. For long periods, large dosing ratios are more effective than similar ratios for short periods. We also compare periodic to continuous dosing and find that the results also depend on the method of distributing the antibiotic within the dosing cycle.