Mathematical Biosciences and Engineering, 2014, 11(3): 547-571. doi: 10.3934/mbe.2014.11.547.

Primary: 49J15, 92C50; Secondary: 92C45, 34D15.

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

A model of optimal dosing of antibiotic treatment in biofilm

1. Department of Mathematics, Syed Babar Ali School of Science and Engineering, Lahore University of Management Sciences, Lahore
2. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804

Biofilms are heterogeneous matrix enclosed micro-colonies ofbacteria mostly found on moist surfaces. Biofilm formation is theprimary cause of several persistent infections found in humans. Wederive a mathematical model of biofilm and surrounding fluiddynamics to investigate the effect of a periodic dose of antibioticon elimination of microbial population from biofilm. The growth rateof bacteria in biofilm is taken as Monod type for the limitingnutrient. The pharmacodynamics function is taken to be dependentboth on limiting nutrient and antibiotic concentration. Assumingthat flow rate of fluid compartment is large enough, we reduce thesix dimensional model to a three dimensional model. Mathematicallyrigorous results are derived providing sufficient conditions fortreatment success. Persistence theory is used to derive conditionsunder which the periodic solution for treatment failure is obtained. We also discuss the phenomenon of bi-stability where both infection-free state and infection state are locally stable when antibiotic dosing is marginal. In addition, we derive the optimal antibiotic application protocols for different scenarios using control theory and show that such treatments ensure bacteria elimination for a wide variety of cases. The results show that bacteria are successfully eliminated if the discrete treatment is given at an early stage in the infection or if the optimal protocol is adopted. Finally, we examine factors which if changed can result in treatment success of the previously treatment failure cases for the non-optimal technique.
  Figure/Table
  Supplementary
  Article Metrics

Keywords perturbation; Antibiotic treatment; stability.; biofilm; bactericidal; persistence

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

References

  • 1. IEEE Trans. Plasma Science, 34 (2006), 1304-1308.
  • 2. Antimicrob Agents Chemotherapy, 44 (2000), 1818-1824.
  • 3. J. Theor. Biol., 194 (1998), 313-339.
  • 4. B. Math. Biol., 67 (2005), 831-853.
  • 5. J. Theor. Biol., 238 (2006), 694-703.
  • 6. J. Theor. Biol., 248(2) (2007), 340-349.
  • 7. EMS Microbiol. Lett., 322 (2011), 1-7.
  • 8. Antimicrob Agents Chemotherapy, 248 (2012), 4816-4826.
  • 9. Antimicrob Agents Chemotherapy, 33 (1989), 535-540.
  • 10. Antimicrob Agents Chemotherapy, 29 (1986), 797-802.
  • 11. Clinical Infectious Diseases, 26 (1998), 1-12.
  • 12. J. Math. Biol., 59 (2009), 563-579.
  • 13. Clin. Microbiol. Rev., 15(2) (2002), 167-193.
  • 14. Clin. Orthop Relat. Res., 437 (2005), 59-66.
  • 15. E. J. Differential Equations, 32 (1998), 1-12.
  • 16. Springer-Verlag, New York, 1975.
  • 17. Expert Opin. Drug Metabolism and Toxi., 1 (2005), 351-361.
  • 18. Nature Review Microbiology, 2 (2004), 95-108.
  • 19. Proc. Amer. Math. Soc., 107 (1989), 1137-1142.
  • 20. Pharmac. Ther., 16 (1982), 143-166.
  • 21. Mathematical Biosciences, 187 (2004), 53-91.
  • 22. Computational and Mathematical Methods in Medicine, 7 (2006), 229-263.
  • 23. Mathematics for Ecology and Environmental Sciences, Springer-Verlag, New York, 2007.
  • 24. Discrete and continous dynamical systems-series B, 8 (2007), 127-143.
  • 25. Discrete and Continuous Dynamical Sustems, 2 (2002), 473-482.
  • 26. J. Math. Biol., 35 (1997), 775-792.
  • 27. Springer-Verlag, New York, 1995.
  • 28. Chapman & Hall/CRC, Taylor & Francis Group, 2007
  • 29. J. Theor. Biology, 122 (1986), 83-92.
  • 30. Antimicrob. Agents Chemother., 54 (2010), 3414-3426.
  • 31. Antimicrob. Agents Chemother., 45 (2001), 999-1007.
  • 32. Scand. J. Infect. Dis. Suppl., 74 (1990), 15-22.
  • 33. Antimicrob Agents Chemother., 51(12) (2007), 4255-4260.
  • 34. Bull. Math. Biol., 74 (2012), 908-934.
  • 35. Antimicrob. Agents Chemother., 48 (2004), 3670-3676.
  • 36. Antimicrob. Agents Chemother., 48 (2004), 48-52.
  • 37. Topics in Advanced Practice Nursing eJournal, 5 (2005).
  • 38. Diff. and Integ. Equations, 8 (1995), 2125-2144.
  • 39. Antimicrob Agents Chemotherapy, 38 (1994), 1052-1058.
  • 40. Antimicrob Agents Chemotherapy, 40 (1996), 2517-2522.
  • 41. SIAM J. Math. Anal., 24 (1993), 407-435.
  • 42. Reviews of Infectious Disease, 8 (1986), 279-291.
  • 43. Journal of General Microbiology, 132 (1986), 1297-1304.
  • 44. Antimicrob. Agents Chemotherapy, 49 (2005), 775-792.
  • 45. World Journal of Modelling and Simulation, 47 (2008), 235-245.
  • 46. Nat. Rev., Microbiol., 7 (2009), 460-466.

 

This article has been cited by

  • 1. Barbara Szomolay, N. G. Cogan, Modelling mechanical and chemical treatment of biofilms with two phenotypic resistance mechanisms, Environmental Microbiology, 2015, 17, 6, 1870, 10.1111/1462-2920.12710
  • 2. Iona K. Paterson, Andy Hoyle, Gabriela Ochoa, Craig Baker-Austin, Nick G. H. Taylor, Optimising Antibiotic Usage to Treat Bacterial Infections, Scientific Reports, 2016, 6, 1, 10.1038/srep37853
  • 3. Maryam Ghasemi, Burkhard A. Hense, Hermann J. Eberl, Christina Kuttler, Simulation-Based Exploration of Quorum Sensing Triggered Resistance of Biofilms to Antibiotics, Bulletin of Mathematical Biology, 2018, 80, 7, 1736, 10.1007/s11538-018-0433-3
  • 4. Sulav Duwal, Stefanie Winkelmann, Christof Schütte, Max von Kleist, Victor De Gruttola, Optimal Treatment Strategies in the Context of ‘Treatment for Prevention’ against HIV-1 in Resource-Poor Settings, PLOS Computational Biology, 2015, 11, 4, e1004200, 10.1371/journal.pcbi.1004200
  • 5. ADNAN KHAN, MUDASSAR IMRAN, OPTIMAL DOSING STRATEGIES AGAINST SUSCEPTIBLE AND RESISTANT BACTERIA, Journal of Biological Systems, 2018, 26, 01, 41, 10.1142/S0218339018500031
  • 6. Philip S Stewart, Tianyu Zhang, Ruifang Xu, Betsey Pitts, Marshall C Walters, Frank Roe, Judith Kikhney, Annette Moter, Reaction–diffusion theory explains hypoxia and heterogeneous growth within microbial biofilms associated with chronic infections, npj Biofilms and Microbiomes, 2016, 2, 1, 10.1038/npjbiofilms.2016.12
  • 7. Maryam Ghasemi, Hermann J. Eberl, Time Adaptive Numerical Solution of a Highly Degenerate Diffusion–Reaction Biofilm Model Based on Regularisation, Journal of Scientific Computing, 2018, 74, 2, 1060, 10.1007/s10915-017-0483-y
  • 8. Nihan Acar, Nick G. Cogan, Enhanced Disinfection of Bacterial Populations By Nutrient and Antibiotic Challenge Timing, Mathematical Biosciences, 2019, 10.1016/j.mbs.2019.04.007

Reader Comments

your name: *   your email: *  

Copyright Info: 2014, Mudassar Imran, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved