Understanding mechanisms of bacterial eradication is critically important for overcoming failures of antibiotic treatments. Current studies suggest that the clearance of large bacterial populations proceeds deterministically, while for smaller populations the stochastic effects become more relevant. Here we develop a theoretical approach to investigate the bacterial population dynamics under the effect of antibiotic drugs using a method of first-passage processes. It allows us to explicitly evaluate the most important characteristics of the bacterial clearance dynamics such as extinction probabilities and extinction times. The new meaning of minimal inhibitory concentrations for stochastic clearance of bacterial populations is also discussed. In addition, we investigate the effect of fluctuations in the population growth rates on dynamics of bacterial eradication. It is found that extinction probabilities and extinction times generally do not correlate with each other when random fluctuations in the growth rates are taking place. Unexpectedly, for a significant range of parameters the extinction times increase due to these fluctuations, indicating a slowing in the bacterial clearance dynamics. It is argued that this might be one of the initial steps in the pathway for the development of antibiotic resistance. Furthermore, it is suggested that extinction times is a convenient measure of bacterial tolerance. 12 1/18 Majority of current experimental and theoretical studies focus on the eradication of 13 initially large quantities of bacteria [14,25,28], and it was shown that a deterministic 14 picture describes well the decrease in these bacterial populations [10,28]. In this 15 deterministic framework, the dynamics of bacterial population exposed to antibiotic is 16 characterized by a minimum inhibitory concentration (MIC), the minimal drug 17 concentration required to inhibit bacterial growth [10,13,28]. The MIC can be regarded 18 as a threshold on the antibiotic concentration such that only above MIC a bacterial 19 population can undergo full extinction, while for concentrations below MIC the infection 20 will never disappear.
21However, it can be argued that it is also critically important to investigate the 22 clearance dynamics for small bacterial populations. Failure to completely eradicate a 23 population of bacteria can have two main consequences. First, even a small number of 24 surviving bacteria can restore infections [19]. Second, certain strains of surviving cells 25 may develop antibiotic resistance, which, in turn, can complicate subsequent 26 therapies [11,17,20]. Therefore, the effective treatment of infections requires not only 27 reducing a large population number to a small number, but also the complete 28 eradication of the bacterial population [4,32,35].
29Despite earlier technical problems [14,25], recent experiments were able to 30 quantitatively investigate the antibiotic-induced clearance of small bacterial 31 populations [9]. It was demonstrated that stochastic factors play much more impo...