Toxin-antitoxin modules are ubiquitous in microbial genomes. They consists of a stable toxic protein interacting with an unstable protein. The function of such modules is yet unknown. We have studied the $HipAB$ system which is a particular example of a Toxin-antitoxin module involved in the phenomenon of bacterial to antibiotic treatments. In contrast to resistance, which is genetically acquired, persistence is a transient phenotypic recalcitrance to antibiotics, observed in only a small fraction of the bacterial population. Experiments performed in the lab of Dr. Nathalie Balaban have showed that persister bacteria are in a dormant state. We have proposed a stochastic model that takes into account the biochemical interactions between the toxin and antitoxin proteins and predicts various properties of the system, such as the fraction of persisters and the distribusion of the lag time (time it takes the bacteria to exit from the dormant state). In particular we have studied the difference between wild type bacteria and an high persistence mutant. Our results agree very nicely with experimental ones.