Modeling the role of altruism of antibiotic-resistant bacteria (Q2447553)

Based on the new findings in a recent experimental study [\textit{H. H. Lee} et al., ``Bacterial charity work leads to population-wide resistance'', Nature 467, 82--86 (2010; \url{doi:10.1038/nature09354})], showing that antibiotic resistant mutants of bacteria produce indoles to protect the wild strain bacteria, the authors propose a mathematical model to describe the evolution of the wild strain, resistant strain and indoles with limited nutrient. The authors distinguish two cases: (i) the mutation is negligible and a resistant strain preexists; (ii) the mutation is not negligible. For (i), the authors 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 [loc.\,cit.]. Further analysis and simulations also reveal some new phenomena not reported in [loc.\,cit.], 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.