Uniform persistence and periodic solution of chemostat-type model with antibiotic

Kaifa Wang; Aijun Fan

doi:10.3934/dcdsb.2004.4.789

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2004, Volume 4, Issue 3: 789-795. Doi: 10.3934/dcdsb.2004.4.789

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Uniform persistence and periodic solution of chemostat-type model with antibiotic

Kaifa Wang^1, and
Aijun Fan¹

1.
Department of Mathematics, College of Medicine, Third Military Medical University, Chongqing, 400038

Received: November 30, 2002

Revised: December 31, 2003

Published: July 2005

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Abstract

A system of functional differential equations is used to model the single microorganism in the chemostat environment with a periodic nutrient and antibiotic input. Based on the technique of Razumikhin, we obtain the sufficient condition for uniform persistence of the microbial population. For general periodic functional differential equations, we obtain a sufficient condition for the existence of periodic solution, therefore, the existence of positive periodic solution to the chemostat-type model is verified.

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Mathematics Subject Classification: 34C25, 92D25.

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