中文摘要：

文章建立了一个生物数学模型,用以描述抗生素耐药性菌株通过释放吲哚,帮助野生菌株在抗生素环境下生存的新现象.该模型中假设菌株有相同的增长率.给出了野生菌株可以一致持久生存的条件,很好地解释了这一生物现象.另外,在一定的条件下,2个菌株可以稳定的共存.而且,数值模拟显示,本模型在一定条件下可以出现Hopf分支现象,从而导致周期解的存在.

英文摘要：

In this paper , a new model is established to describe a novel phenomenon that ant ibiot ic-resistant bacteria can help wild bacteria survive under antibiotic stress through releasing indoles. In this model, bacteria strains are assumed to have the same growth rate. We established conditions that the wild bacteria can be uni-formly persistent, which is wel l match the novel phenomenon above. Besides, both strains are coexistent stably under certain conditions. Numerical simulations show that our model may undergo a Hopf bifurcation, leading to the existence of periodic solutions.