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  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X
 

Dynamics of a delay differential equation model of phage growth in two-stage chemostat


Authors: Huiyan Zhu and Yang Luo
Journal: Quart. Appl. Math. 70 (2012), 299-310
MSC (2010): Primary 92B05, 92C17; Secondary 92D25
Published electronically: February 14, 2012
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Abstract: In this paper, we consider a mathematical model for phage growth in a two-stage chemostat, taking account of the delay from infection to lysis. We give sufficient conditions for the globally asymptotic stability of noninfected equilibrium and obtain sufficient conditions for the local stability of infected equilibrium. We also perform some numerical simulations which illustrate the theoretical results obtained. The formula for $ \mathcal R_0 $ shows that decreasing the delay and/or increasing the burst size will increase $ \mathcal R_0 $.


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Additional Information

Huiyan Zhu
Affiliation: College of Mathematics-Physics, University of South China, Hengyang, Hunan 421001, People’s Republic of China
Email: zhuhuiyan@126.com

Yang Luo
Affiliation: College of Computer Science and Technology, University of South China, Hengyang, Hunan 421001, People’s Republic of China
Email: luoyang@usc.edu.cn

DOI: http://dx.doi.org/10.1090/S0033-569X-2012-01266-5
PII: S 0033-569X(2012)01266-5
Keywords: Dynamics, delay differential equation, stability, phage, two-stage chemostat
Received by editor(s): September 10, 2010
Published electronically: February 14, 2012
Additional Notes: Research supported by Hunan Provincial Natural Science Foundation of China (No. 11JJ9001), the Natural Science Foundation of China (No. 11071060), and the project of Hunan Provincial Science & Technology Department (No. 2010GK3013).
Article copyright: © Copyright 2012 Brown University
The copyright for this article reverts to public domain 28 years after publication.



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