SavedAdd your journal

Journals / International Journal of Engineering and Applied Sciences / 2026 / Volume: 10 Issue: 2

On The Stability Analysis of The General Mathematical Modeling of Bacterial Infection

Bahatdin Daşbaşı(Kayseri University)
İlhan Öztürk(Erciyes University)
Pages
—
Publication Date
2018-08-15
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In addition that, results of the analysis have supported by numerical simulations.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, a mathematical model examined the dynamics among populations of sensitive bacteria and resistant bacteria to antibiotic, antibiotic concentration and hosts immune system cells in an individual (or host), received antibiotic therapy in the case of a local bacterial infection, was proposed.
📊
Key Findings & Data:Stability analysis of this model have been also performed.
💡
Conclusion & Impact:In addition that, results of the analysis have supported by numerical simulations.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Mathematical model · Stability analysis · Numerical simulation

Abstract

In this study, a mathematical model examined the dynamics among populations of sensitive bacteria and resistant bacteria to antibiotic, antibiotic concentration and hosts immune system cells in an individual (or host), received antibiotic therapy in the case of a local bacterial infection, was proposed. Stability analysis of this model have been also performed. In addition that, results of the analysis have supported by numerical simulations.

🔖

Cite This Article

Daşbaşı, B., Öztürk, İ. (2018). On The Stability Analysis of The General Mathematical Modeling of Bacterial Infection. International Journal of Engineering and Applied Sciences, Volume: 10 Issue: 2. https://doi.org/10.24107/ijeas.445520

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (32)

  1. Mondragón, E.I., Mosquera, S., Cerón, M., Burbano-Rosero, E.M., Hidalgo-Bonilla, S.P., Esteva, L., P.R-L Jhoana, Mathematical modeling on bacterial resistance to multiple antibiotics caused by spontaneous mutations, BioSystems, 117, 60–67, 2014. Daşbaşı, B. and Öztürk, İ., Mathematical modelling of bacterial resistance to multiple antibiotics and immune system response, SpringerPlus, 5, 1-17, 2016.
  2. Mahmoud, A. G. and Rice, L. B., Antifungal agents: mode of action, mechanisms of resistance, and correlation of these mechanisms with bacterial resistance, and correlation, Clin. Microbiol. Rev., 12(4), 501–517, 1999.
  3. Murray, J.D., Mathematical Biology. I. An introduction, Springer-Verlag, 3rd Edition, 2002.
  4. Murray, J.D., Mathematical Biology. II: Spatial Models and Biomedical Applications, Springer-Verlag, 3rd Edition, 2003.
  5. Daşbaşı, B., The Fractional-Order mathematical modeling of bacterial resistance against multiple antibiotics in case of local bacterial infection, Sakarya University Journal of Science, 251, 1-13, 2017.
  6. Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K. and Walter, P.P., Molecular Biology of the Cell. The Adaptive Immune System, Garland Science, 4th Edition, 2002.
  7. Hethcote, H.W., The mathematics of infectious diseases, SIAM Rev., 42, 599-653, 2000.
  8. Austin, D., Kakehashi, M. and Anderson, R.M., The transmission dynamics of antibiotic-resistant bacteria: The relationship between resistance in commensal organisms and antibiotic consumption, Proc. R. Soc. Lond. [Biol.], 264, 1629–1638, 1997.
  9. Bonten, M., Austin, J. and Lipsitch, M., Understanding the spread of antibiotic resistant pathogens in hospitals, mathematical models as tools for control, Clin. Infect. Dis, 33, 1739-1746, 2001.
  10. Austin, D. and Anderson, R., Studies of antibiotic resistance within the patient, hospitals and the community using simple mathematical models, Philos. Trans. R. Soc. Lond. [Biol.], 354, 721–738, 1999.
  11. Imran, M. and Smith, H., The pharmaco dynamics of antibiotic treatment, Comput. Math. Method Med., 7, 229–263, 2006.
  12. Alanis, A., Resistance to antibiotics: are we in the post-antibioticera?, Arch. Med. Res., 36, 697-705, 2005.
  13. Tenover, F., Mechanisms of antimicrobial resistance in bacteria, Am. J. Med., 119, 3–10, 2006.
  14. Bergstrom, C., Lipsitch, M. and Levin, B., Natural selection, infectious transfer and the existence conditions for bacterial plasmids, Genetics, 155, 1505–1519, 2000.
  15. D'Agata, E., Dupont-Rouzeyrol, M., Magal, P., Olivier, D. and Ruan, S., The impact of different antibiotic regimens on the emergence of antimicrobial-resistant bacteria, PLOSone, 3, 1-9, 2008.
  16. Imran, M. and Smith, H., The dynamics of bacterial infection, innate immune response, and antibiotic treatment, Discrete Contin. Dyn. Syst. B, 8, 127–147, 2007.
  17. Whitman, A. and Ashrafiuon, H., Asymptotic theory of an infectious disease model, J. Math. Biol., 53, 287-304, 2006.
  18. Lipsitch, M. and Levin, B., The population dynamics of antimicrobial chemotherapy, Antimicrob. Agents Ch., 41, 363–373, 1997.
  19. Nikolaou, M. and Tam, V., A new modeling approach to the effect of antimicrobial agents on heterogeneous microbial populations, J. Math. Biol., 52, 154–182, 2006.
  20. Allen, L.J.S., An Introduction to Mathematical Biology, London: Pearson Education, 2007.
  21. Hale, J. and Koçak, H., Dynamics and Bifurcations, New York: Springer-Verlag, 1991.
  22. Handel, A., Margolis, E. and Levin, B., Exploring the role of the immune response in preventing antibiotic resistance, J.Theor.Biol., 256, 655–662, 2009.
  23. Antunes, L.C.S., Imperi, F., Carattoli, A. and Visca, P., Deciphering the Multifactorial Nature of Acinetobacter baumannii Pathogenicity, PLOSone, 6, 2011.
  24. Freter, R., Freter, R.R. and Brickner, H., Experimental and mathematical models of Escherichia coli plasmid transfer in vitro and in vivo, Infect. Immun., 39, 60-84, 1985.
  25. Ternent, L., Dyson, R.J., Krachler, A.M. and Jabbari, S., Bacterial fitness shapes the population dynamics of antibiotic resistant and susceptible bacteria in a model, J. Theor. Biol., 372, 1-11, 2014.
  26. Pugliese, A. and Gandolfi, A., A simple model of pathogen–immune dynamics including specific and non-specific immunity, Math. Biosci., 214, 73–80, 2008.
  27. Smith, A., McCullers, J. and Adler, F., Mathematical model of a three-stage innate immune response to a pneumococcal lung infection, J. Theor. Biol., 276, 106–116, 2011.
  28. Alavez, J., Avenda, R., Esteva, L., Fuentes, J., Garcia, G. and Gómez, G., Within-host population dynamics of antibiotic-resistant M. Tuberculosis, Math. Med. Biol., 24, 35-56, 2006.
  29. Campion, J.J., McNamara, P.J. and Evans, M.E., Evolution of Ciprofloxacin-Resistant Staphylococcus aureus in In Vitro, Antimicrob. Agents Ch., 48, 4733–4744, 2004.
  30. Carruthers, M. D., Nicholson, P. A., Tracy, E. N. and Munson, R. S., Acinetobacter baumannii Utilizes a Type VI Secretion System for Bacterial Competition, PLOSone, 8, 1-8, 2013.
  31. McGrath, M., Pittius, N. C., Helden, P.D., Warren, R.M. and Warner, D.F., Mutation rate and the emergence of drug resistance inMycobacterium tuberculosis, J. Antimicrob. Chemoth., 69, 292-302, 2014.
  32. Ryan, C.T. and Romesberg, F.E., Induction and Inhibition of Ciprofloxacin Resistance-Conferring Mutations in Hypermutator Bacteria, Antimicrob. Agents Ch., 50, 220–225, 2006.