  It has long been known that antibiotic treatment will not completely kill off
a bacteria population. For many species a small fraction of bacteria is not
sensitive to antibiotics. These bacteria are said to persist. Recently it has
been shown that persistence is not a permanent state and that in fact a
bacterium can switch back and forth between persistent and non persistent
states. We introduce two stochastic models for bacteria persistence. In both
models there are mass killings of non persistent bacteria at certain times. The
first model has deterministic killing times and the second one has random
killing times. Both models suggest that persistence may be a successful
strategy for a wide range of parameter values.
