August  2004, 4(3): 789-795. doi: 10.3934/dcdsb.2004.4.789

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

1. 

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

Received  December 2002 Revised  January 2004 Published  May 2004

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.
Citation: Kaifa Wang, Aijun Fan. Uniform persistence and periodic solution of chemostat-type model with antibiotic. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 789-795. doi: 10.3934/dcdsb.2004.4.789
[1]

Liang Kong, Tung Nguyen, Wenxian Shen. Effects of localized spatial variations on the uniform persistence and spreading speeds of time periodic two species competition systems. Communications on Pure & Applied Analysis, 2019, 18 (4) : 1613-1636. doi: 10.3934/cpaa.2019077

[2]

Paul L. Salceanu. Robust uniform persistence in discrete and continuous dynamical systems using Lyapunov exponents. Mathematical Biosciences & Engineering, 2011, 8 (3) : 807-825. doi: 10.3934/mbe.2011.8.807

[3]

Keng Deng, Yixiang Wu. Extinction and uniform strong persistence of a size-structured population model. Discrete & Continuous Dynamical Systems - B, 2017, 22 (3) : 831-840. doi: 10.3934/dcdsb.2017041

[4]

P.E. Kloeden, Desheng Li, Chengkui Zhong. Uniform attractors of periodic and asymptotically periodic dynamical systems. Discrete & Continuous Dynamical Systems - A, 2005, 12 (2) : 213-232. doi: 10.3934/dcds.2005.12.213

[5]

Antoine Perasso. Global stability and uniform persistence for an infection load-structured SI model with exponential growth velocity. Communications on Pure & Applied Analysis, 2019, 18 (1) : 15-32. doi: 10.3934/cpaa.2019002

[6]

Kazuo Yamazaki, Xueying Wang. Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic model. Mathematical Biosciences & Engineering, 2017, 14 (2) : 559-579. doi: 10.3934/mbe.2017033

[7]

Carlota Rebelo, Alessandro Margheri, Nicolas Bacaër. Persistence in some periodic epidemic models with infection age or constant periods of infection. Discrete & Continuous Dynamical Systems - B, 2014, 19 (4) : 1155-1170. doi: 10.3934/dcdsb.2014.19.1155

[8]

Zhijun Liu, Weidong Wang. Persistence and periodic solutions of a nonautonomous predator-prey diffusion with Holling III functional response and continuous delay. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 653-662. doi: 10.3934/dcdsb.2004.4.653

[9]

Xinlong Feng, Yinnian He. On uniform in time $H^2$-regularity of the solution for the 2D Cahn-Hilliard equation. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5387-5400. doi: 10.3934/dcds.2016037

[10]

Masaki Kurokiba, Toshitaka Nagai, T. Ogawa. The uniform boundedness and threshold for the global existence of the radial solution to a drift-diffusion system. Communications on Pure & Applied Analysis, 2006, 5 (1) : 97-106. doi: 10.3934/cpaa.2006.5.97

[11]

Claudianor O. Alves. Existence of periodic solution for a class of systems involving nonlinear wave equations. Communications on Pure & Applied Analysis, 2005, 4 (3) : 487-498. doi: 10.3934/cpaa.2005.4.487

[12]

Jingli Ren, Zhibo Cheng, Stefan Siegmund. Positive periodic solution for Brillouin electron beam focusing system. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 385-392. doi: 10.3934/dcdsb.2011.16.385

[13]

Mi-Young Kim. Uniqueness and stability of positive periodic numerical solution of an epidemic model. Discrete & Continuous Dynamical Systems - B, 2007, 7 (2) : 365-375. doi: 10.3934/dcdsb.2007.7.365

[14]

Changrong Zhu, Bin Long. The periodic solutions bifurcated from a homoclinic solution for parabolic differential equations. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3793-3808. doi: 10.3934/dcdsb.2016121

[15]

Gui-Dong Li, Yong-Yong Li, Xiao-Qi Liu, Chun-Lei Tang. A positive solution of asymptotically periodic Choquard equations with locally defined nonlinearities. Communications on Pure & Applied Analysis, 2020, 19 (3) : 1351-1365. doi: 10.3934/cpaa.2020066

[16]

Ming Mei, Yau Shu Wong, Liping Liu. Phase transitions in a coupled viscoelastic system with periodic initial-boundary condition: (I) Existence and uniform boundedness. Discrete & Continuous Dynamical Systems - B, 2007, 7 (4) : 825-837. doi: 10.3934/dcdsb.2007.7.825

[17]

Michele L. Joyner, Cammey C. Manning, Whitney Forbes, Michelle Maiden, Ariel N. Nikas. A physiologically-based pharmacokinetic model for the antibiotic ertapenem. Mathematical Biosciences & Engineering, 2016, 13 (1) : 119-133. doi: 10.3934/mbe.2016.13.119

[18]

Mudassar Imran, Hal L. Smith. A model of optimal dosing of antibiotic treatment in biofilm. Mathematical Biosciences & Engineering, 2014, 11 (3) : 547-571. doi: 10.3934/mbe.2014.11.547

[19]

Yongkun Li, Pan Wang. Almost periodic solution for neutral functional dynamic equations with Stepanov-almost periodic terms on time scales. Discrete & Continuous Dynamical Systems - S, 2017, 10 (3) : 463-473. doi: 10.3934/dcdss.2017022

[20]

Jing Li, Boling Guo, Lan Zeng, Yitong Pei. Global weak solution and smooth solution of the periodic initial value problem for the generalized Landau-Lifshitz-Bloch equation in high dimensions. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 0-0. doi: 10.3934/dcdsb.2019230

2018 Impact Factor: 1.008

Metrics

  • PDF downloads (12)
  • HTML views (0)
  • Cited by (4)

Other articles
by authors

[Back to Top]