Competition in a chemostat with wall attachment

SIAM Journal on Applied Mathematics

Volumn 61, Issue 2, 2000, Pages 567-595

  Stemmons, Eric D ^a   Smith, Hal L ^a  

^a ARIZONA STATE UNIVERSITY   (United States)

Author keywords

Chemostat; Colonization resistance; Competition for wall attachment sites; Uniform persistence

Indexed keywords

BACTERIA; BACTERIOLOGY; COMPETITION; MATHEMATICAL MODELS; NUTRITION;

COLONIZATION RESISTANCE;

CHEMOSTATS;

EID: 0342936164     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139999358131     Document Type: Article

References (27)

1. M. BALLYK AND H. L. SMITH, A flow reactor with wall growth, in Mathematical Models in Medical and Health Sciences, M. Horn, G. Simonett, and G. Webb, eds., Vanderbilt University Press, Nashville, TN, 1998.
2. M. BALLYK AND H. L. SMITH, A model of microbial growth in a plug flow reactor with wall attachment, Math. Biosci., 158 (1999), pp. 95-126.
3. M. BALLYK, D. LE, D. JONES, AND H. L. SMITH, Effects of random motility on microbial growth and competition in a flow reactor, SIAM J. Appl. Math., 59 (1998), pp. 573-596.
4. B. BALTZIS AND A. FREDERICKSON, Competition of two microbial populations for a single resource in a chemostat when one of them exhibits wall attachment, Biotechnology and Bioengineering, 25 (1983), pp. 2419-2439.
5. W. G. CHARACKLIS AND K. C. MARSHALL, EDS., Biofilms, Wiley Series in Ecological and Applied Microbiology, John Wiley and Sons, New York, 1990.
6. P. L. CONWAY, Microbial ecology of the human large intestine, in Human Colonic Bacteria, Role in Nutrition, Physiology, and Pathology, G. R. Gibson and G. T. Macfarlane, eds., CRC Press, Boca Raton, FL, 1995.
7. J. COSTERTON, Z. LEWANDOWSKI, D. DEBEER, D. CALDWELL, D. KORBER, AND G. JAMES, Biofilms, the customized microniche, J. Bacteriology, 176 (1994), pp. 2137-2142.
8. J. COSTERTON, Z. LEWANDOWSKI, D. CALDWELL, D. KORBER, AND H. LAPPIN-SCOTT, Microbial biofilms, Ann. Rev. Microbiology, 49 (1995), pp. 711-745.
9. J. COSTERTON, P. STEWART, AND E. GREENBERG Bacterial biofilms: A common cause of persistent infections, Science, 284 (1999), pp. 1318-1322.
10. R. FRETER, E. STAUFFER, E. CLEVEN, L. HOLDEMAN, AND W. MOORE, Continuous-flow cultures as in vitro models of the ecology of large intestinal flora, Infection and Immunity, 39 (1983), pp. 666-675.
11. R. FRETER, H. BRICKNER, J. FEKETE, M. VICKERMAN, AND K. CAREY, Survival and implantation of Escherichia coli in the intestinal tract, Infection and Immunity, 39 (1983), pp. 686-703.
12. R. FRETER, Mechanisms that control the microflora in the large intestine, in Human Intestinal Microflora in Health and Disease, D. Hentges, ed., Academic Press, New York, 1983.
13. R. FRETER, The need for mathematical models in understanding colonization and plasmid transfers in the mammalian intestine, Banbury Report, 24 (1983), pp. 81-93.
14. R. FRETER, Interdependence of mechanisms that control bacterial colonization of the large intestine, Microecology and Therapy, 14 (1984), pp. 89-96.
15. R. FRETER, H. BRICKNER, AND S. TEMME, An understanding of colonization resistance of the mammalian large intestine requires mathematical analysis, Microecology and Therapy, 16 (1986), pp. 147-155.
16. J. K. HALE, Ordinary Differential Equations, Krieger Publishing, Malabar, FL, 1980.
17. D. JONES AND H. L. SMITH, Microbial competition for nutrient and wall sites in plug flow, SIAM J. Appl. Math., 60 (2000), pp. 1576-2000.
18. A. LEE, Neglected Niches: The Microbial Ecology of the Gastrointestinal Tract, in Advances in Microbial Ecology, K. C. Marshall, ed., Plenum Press, New York, 1985.
19. G. T. MACFARLANE, S. MACFARLANE, AND G. R. GIBSON, Validation of a three-stage compound continuous culture system for investigating the effect of retention time in the ecology and metabolism of bacteria in the human colon, Microbial Ecology, 35 (1998), pp. 180-187.
20. S. PILYUGIN AND P. WALTMAN, The simple chemostat with wall growth, SIAM J. Appl. Math., 59 (1999), pp. 1552-1572.
21. R. ROLFE, Colonization resistance, in Gastrointestinal Microbiology, Vol 2, R. Mackie, B. White, R. Isaacson, eds., Chapman and Hall Microbiology Series, Chapman and Hall, New York, 1997.
22. D. C. SAVAGE, Microbial ecology of the gastrointestinal tract, Ann. Rev. Microbiology, 31 (1977), pp. 107-133.
23. H. L. SMITH AND P. WALTMAN, The Theory of the Chemostat, Cambridge University Press, Cambridge, UK, 1995.
24. H. L. SMITH, Monotone Dynamical Systems, an Introduction to the Theory of Competitive and Cooperative Systems, Math. Surveys Monogr. 41, Amer. Math. Soc., Providence, RI, 1995.
25. E. D. STEMMONS, Competition in a Chemostat with Wall Growth, Ph.D. thesis, Arizona State University, Tempe, AZ, 1999.
26. H. THIEME. Persistence under relaxed point-dissipativity (with application to an endemic model), SIAM J. Math. Anal., 24 (1993), pp. 407-435.
27. H. TOPIWALA AND G. HAMER, Effect of wall growth in steady-state continuous cultures, Biotechnology and Bioengineering, 13 (1971), pp. 919-922.