Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Persistence in phage-bacteria communities with nested and one-to-one infection networks

Pages: 859 - 875, Volume 22, Issue 3, May 2017      doi:10.3934/dcdsb.2017043

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Dan A. Korytowski - School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, United States (email)
Hal L. Smith - Department of Mathematics and Statistics, Arizona State University, Tempe, AZ, 85287, United States (email)

Abstract: We show that a bacteria and bacteriophage system with either a perfectly nested or a one-to-one infection network is permanent, a.k.a uniformly persistent, provided that bacteria that are superior competitors for nutrient devote the least to defence against infection and the virus that are the most efficient at infecting host have the smallest host range. By ensuring that the density-dependent reduction in bacterial growth rates are independent of bacterial strain, we are able to arrive at the permanence conclusion sought by Jover et al [3]. The same permanence results hold for the one-to-one infection network considered by Thingstad [9] but without virus efficiency ordering. In some special cases, we show the global stability for the nested infection network, and obtain restrictions on the global dynamics for the one-to-one network.

Keywords:  Persistence, permanence, community assembly, phage-bacteria infection network, nested infection network, Lyapunov function.
Mathematics Subject Classification:  Primary: 92D40; Secondary: 37B25.

Received: August 2015;      Revised: January 2016;      Available Online: January 2017.