# American Institute of Mathematical Sciences

July  2009, 12(1): 227-250. doi: 10.3934/dcdsb.2009.12.227

## Normal and slow growth states of microbial populations in essential resource-based chemostat

 1 Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026 2 Department of Mathematics, Xinjiang Normal University, Urmuqi, 830054, China

Received  November 2008 Revised  January 2009 Published  May 2009

To mimic the striking capability of microbial culture for growth adaptation after the onset of the novel environmental conditions, a modified heterogeneous microbial population model in the chemostat with essential resources is proposed which considers adaptation by spontaneously phenotype-switching between normally growing cells and persister cells having reduced growth rate. A basic reproductive number $R_0$ is introduced so that the population dies out when $R_0<1$, and when $R_0>1$ the population will be asymptotic to a steady state of persister cells, or a steady state of only normal cells, or a steady state corresponding to a heterogeneous population of both normal and persister cells. Our analysis confirms that inherent heterogeneity of bacterial populations is important in adaption to fluctuating environments and in the persistence of bacterial infections.
Citation: Yi Wang, Chengmin Zheng. Normal and slow growth states of microbial populations in essential resource-based chemostat. Discrete & Continuous Dynamical Systems - B, 2009, 12 (1) : 227-250. doi: 10.3934/dcdsb.2009.12.227
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