title: Modeling the role of altruism of antibiotic-resistant bacteria.
abstract: Based on the new findings in a recent experimental study (Lee et al., Nature 467, 82-86, 2010) that antibiotic resistant mutants of bacteria produce indoles to protect the wild strain bacteria, we propose a mathematical model to describe the evolution of the wild strain, resistant strain and indoles with limited nutrient. We distinguish two cases: (i) mutation is negligible and a resistant strain preexists; (ii) mutation is not negligible. For (i), we establish conditions for co-persistence of both strains, which indicate that the wild strain can survive with the help from the altruistic resistant strain, whereas it dies out in the absence of such a benefit. This consolidates the experimental findings in Lee et al. (Nature 467:82-86 2010). Further analysis and simulations also reveal some new phenomena not reported in Lee et al. (Nature 467:82-86 2010), that is, periodic oscillations of the populations may occur within certain range of the parameters, and there exists bistability in the sense that a stable positive periodic solution coexists with a stable positive equilibrium.
authors.affiliation: Key Laboratory of Eco-environments in Three Gorges Reservoir Region, School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People's Republic of China.
authors.forename: Wendi
authors.initials: W
authors.lastname: Wang
authors.forename: Xingfu
authors.initials: X
authors.lastname: Zou
mesh_terms: D019149:Bioreactors / Q000382:microbiology; D003198:Computer Simulation; D024881:Drug Resistance, Bacterial / Q000502:physiology*; D004926:Escherichia coli / Q000254:growth & development*; D004927:Escherichia coli Infections / Q000188:drug therapy*; D007211:Indoles / Q000378:metabolism*; D008954:Models, Biological
chemical_list: D007211:Indoles
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