  The evolution of antimicrobial resistance can be strongly affected by
variations of antimicrobial concentration. Here, we study the impact of
periodic alternations of absence and presence of antimicrobial on resistance
evolution in a microbial population, using a stochastic model that includes
variations of both population composition and size, and fully incorporates
stochastic population extinctions. We show that fast alternations of presence
and absence of antimicrobial are inefficient to eradicate the microbial
population and strongly favor the establishment of resistance, unless the
antimicrobial increases enough the death rate. We further demonstrate that if
the period of alternations is longer than a threshold value, the microbial
population goes extinct upon the first addition of antimicrobial, if it is not
rescued by resistance. We express the probability that the population is
eradicated upon the first addition of antimicrobial, assuming rare mutations.
Rescue by resistance can happen either if resistant mutants preexist, or if
they appear after antimicrobial is added to the environment. Importantly, the
latter case is fully prevented by perfect biostatic antimicrobials that
completely stop division of sensitive microorganisms. By contrast, we show that
the parameter regime where treatment is efficient is larger for biocidal drugs
than for biostatic drugs. This sheds light on the respective merits of
different antimicrobial modes of action.
