The analysis and regulation for the dynamics of a temperate bacteriophage model

The purpose of this paper is to study the asymptotical behavior of a temperate bacteriophage model in chemostat, which was first proposed by Levin et al. [B.R. Levin, F.M. Stewart, L. Chao, Resource-limited growth, competition and predation: A model and experiment studies with bacteria and bacteriophage, Am. Nat. 125 (1977) 3]. Firstly, a classification for the equilibria of the model and their stability are obtained; secondly, sufficient conditions for uniform persistence are obtained; thirdly, sufficient conditions for the global asymptotic behavior are given, and simulations for the model are presented. The theoretical results show that there are more than eight cases for the classification of the model, and that the decrease (increase) of the nutrient concentration or average lytic time (flow rate) is beneficial to the survival of the sensitive cells. Both the simulated and theoretical results show that there is a possibility of switch phenomena or a periodical outburst of the phages and the lysogens, which is caused by the internal factors rather than by some external environment. Finally, the simulation and regulation of the dynamics of the model with experimental data are presented.