title: Persistent and susceptible bacteria with individual deaths.
abstract: The aim of this paper is to study two models for a bacterial population subject to antibiotic treatments. It is known that some bacteria are not sensitive to antibiotics. These bacteria, called persisters, are in a state called persistence and each bacterium can switch from this state to a non-persistent (or susceptible) state and back (with rates b and a respectively). Our models extend those introduced in Garet et al. (2012) by adding a random natural life cycle for each bacterium and by allowing bacteria in the susceptible state to escape the action of the antibiotic with a fixed probability 1-p (while every bacterium in a persistent state survives with probability 1). This last mechanism of survival to the antibiotics differs from the persistent state one (where reproduction is forbidden) since in this case the bacterium can replicate. We study two different models. In the first model we "inject" the antibiotics in the system at fixed, deterministic times while in the second one the time intervals are random. We show that, in order to kill eventually the whole bacterial population, these time intervals cannot be "too large". The maximum admissible length is increasing with respect to p; we see that even when p is close to 1, this interval length can be significantly smaller than in the case p=1. While in the case p=1 switching back and forth to the persistent state is the only chance of surviving for bacteria, when p<1 and the death rate in the persistent state, say dr, is positive then the situation is more complex. In this case our model suggests that if dr and b are positive (and fixed) then for higher values of p there is an interval for the rate a, say (0,ap) where switching to the persistent state is a good strategy while for a>ap the situation is less favorable than a=0. On the other hand, for smaller values of p the best strategy is a=0, that is, not switching. Finally, when dr=0, switching to the susceptible state is always a better strategy, from the bacterial point of view, than staying in the susceptible state all the times.
authors.affiliation: Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy. Electronic address: fabio.zucca@polimi.it.
authors.forename: Fabio
authors.initials: F
authors.lastname: Zucca
mesh_terms: D000900:Anti-Bacterial Agents / Q000494:pharmacology*; D001419:Bacteria / Q000187:drug effects*; D008826:Microbial Sensitivity Tests; D050296:Microbial Viability / Q000187:drug effects; D008954:Models, Biological; D013997:Time Factors
chemical_list: D000900:Anti-Bacterial Agents
keywords: Bacteria persistence; Multitype branching process; Random environment; Stochastic model