Abstract
A model for three competing bacterial strains that incorporates mutation and/or phenotypic switching is studied. We consider three different strains: wild, mutated and phenotypic bacteria generated by an inhibitor introduced in the environment. Our model considers that all new phenotypic bacteria are sensitive to the inhibitor and there is no phenotypic replication. Two steady state regimes are identified, finding that the strain surviving is the one arising from mutation of the wild strain. The model may also show three steady state regimes with the persistence of the three bacteria in the system.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Balaban, N.Q., Merrin, J, et. al..: Bacterial Persistence as a Phenotypic Switch. Science 305, 1622–1625 (2004)
Braselton, J.P., Waltman, P.: A competition model with dynamically allocated inhibitor production. Mathematical Biosciences 173, 55–84 (2001)
Hsu, S.B., Waltman, P.: A survey of mathematical models of competition with an inhibitor. Mathematical Biosciences 187, 53–91 (2004)
Hsu, S.B., Li, Y.S., Waltman, P.: Competition in the presence of a lethal external inhibitor. Mathematical Biosciences 167, 177–199 (2000)
Hsu, S.B., Waltman, P.: Analysis of a model of two competitors in a chemostat with an external inhibitor. Journal of Applied Mathematics (SIAM) 52, 528–540 (1992)
Hsu, S.B., Waltman, P.: Competition in the chemostat when one competitor produces a toxin. Japaniese Journal of Industrial Applied Mathematics 15, 471–490 (1998)
Khalil, H.: Nonlinear Systems. Prentice-Hall (1996)
Jones, D.A., Le, D., Kojouharov, H.V., Smith, H.L.: The Freter model: A simple model of biofilm formation. Journal of Mathematical Biology 472, 137–152 (2003)
Leenheer, P., Li, B., Smith, H.L.: Competition in the chemostat: Some remarks. Canadian Applied Mathematics Quarterly 113, 229–248 (2003)
Leenheer, P., Smith, H.L.: Feedback control for the chemostat. Journal of Mathematical Biology 46, 48–70 (2003)
Lenski, R.E., Hattingh, S.: Coexistence of two competitors one resource and one inhibitor: a chemostat model based on bacteria and antibiotics. Journal of Theoretical Biology 122, 83–93 (1986)
Levin, B.R.: Noninherited Resistance to Antibiotics. Science 305, 1578–1579 (2004)
Li, B., Smith, H.L.: How Many Species Can Two Essential Resources Support?. Journal of Applied Mathematics (SIAM) 62, 336–366 (2001)
Markus, L.: Asymptotically autonomous differential systems. In: Lefschetz, S. (ed.) Contributions to the theory of Nonlinear Oscillations III. Annals of Mathematics Studies 36 Princeton University Press, Princeton, NJ, 17–29 (1956)
Miller, C., et. al.: SOS Response Induction by β-Lactams and bacterial defense against antibiotic Lethality. Science 305, 1629–1631 (2004)
Smith, H. L., Waltman, P.: The theory of the chemostat. Dynamics of microbial competition. Cambdrige University Press (1995)
Stemmons, E.D., Smith, H.L.: Competition in a chemostat with wall attachment. Journal of Applied Mathematics (SIAM) 612, 567–595 (2000)
Thieme, H.R.: Convergence results and a Poincaé-Bendixon trichotomy for asymtotically autonomous differential equations. Journal of Mathematical Biology 30, 755–763 (1992)
Thieme, H.R.: Mathematics in Population Biology. Princeton University Press, Princeton, NJ (2003)
El ciclo del azufre, http://www.monografias.com/trabajos4/azufre/azufre.shtml.
Mecanismos de resistencia, www.virtual,unal.edu.co/cursos/odontologia/2005205.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Tapia-Santos, B., Velasco-Hernández, J.X. (2008). Phenotypic Switching and Mutation in the Presence of a Biocide: No Replication of Phenotypic Variant. In: Mondaini, R.P., Pardalos, P.M. (eds) Mathematical Modelling of Biosystems. Applied Optimization, vol 102. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76784-8_7
Download citation
DOI: https://doi.org/10.1007/978-3-540-76784-8_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-76783-1
Online ISBN: 978-3-540-76784-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)