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

Year 2018, Volume: 10 Issue: 2, 93 - 117, 15.08.2018
https://doi.org/10.24107/ijeas.445520

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.

References

  • 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.
  • 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.
  • Murray, J.D., Mathematical Biology. I. An introduction, Springer-Verlag, 3rd Edition, 2002.
  • Murray, J.D., Mathematical Biology. II: Spatial Models and Biomedical Applications, Springer-Verlag, 3rd Edition, 2003.
  • 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.
  • 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.
  • Hethcote, H.W., The mathematics of infectious diseases, SIAM Rev., 42, 599-653, 2000.
  • 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.
  • 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.
  • 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.
  • Imran, M. and Smith, H., The pharmaco dynamics of antibiotic treatment, Comput. Math. Method Med., 7, 229–263, 2006.
  • Alanis, A., Resistance to antibiotics: are we in the post-antibioticera?, Arch. Med. Res., 36, 697-705, 2005.
  • Tenover, F., Mechanisms of antimicrobial resistance in bacteria, Am. J. Med., 119, 3–10, 2006.
  • Bergstrom, C., Lipsitch, M. and Levin, B., Natural selection, infectious transfer and the existence conditions for bacterial plasmids, Genetics, 155, 1505–1519, 2000.
  • 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.
  • 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.
  • Whitman, A. and Ashrafiuon, H., Asymptotic theory of an infectious disease model, J. Math. Biol., 53, 287-304, 2006.
  • Lipsitch, M. and Levin, B., The population dynamics of antimicrobial chemotherapy, Antimicrob. Agents Ch., 41, 363–373, 1997.
  • 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.
  • Allen, L.J.S., An Introduction to Mathematical Biology, London: Pearson Education, 2007.
  • Hale, J. and Koçak, H., Dynamics and Bifurcations, New York: Springer-Verlag, 1991.
  • 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.
  • Antunes, L.C.S., Imperi, F., Carattoli, A. and Visca, P., Deciphering the Multifactorial Nature of Acinetobacter baumannii Pathogenicity, PLOSone, 6, 2011.
  • 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.
  • 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.
  • Pugliese, A. and Gandolfi, A., A simple model of pathogen–immune dynamics including specific and non-specific immunity, Math. Biosci., 214, 73–80, 2008.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
Year 2018, Volume: 10 Issue: 2, 93 - 117, 15.08.2018
https://doi.org/10.24107/ijeas.445520

Abstract

References

  • 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.
  • 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.
  • Murray, J.D., Mathematical Biology. I. An introduction, Springer-Verlag, 3rd Edition, 2002.
  • Murray, J.D., Mathematical Biology. II: Spatial Models and Biomedical Applications, Springer-Verlag, 3rd Edition, 2003.
  • 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.
  • 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.
  • Hethcote, H.W., The mathematics of infectious diseases, SIAM Rev., 42, 599-653, 2000.
  • 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.
  • 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.
  • 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.
  • Imran, M. and Smith, H., The pharmaco dynamics of antibiotic treatment, Comput. Math. Method Med., 7, 229–263, 2006.
  • Alanis, A., Resistance to antibiotics: are we in the post-antibioticera?, Arch. Med. Res., 36, 697-705, 2005.
  • Tenover, F., Mechanisms of antimicrobial resistance in bacteria, Am. J. Med., 119, 3–10, 2006.
  • Bergstrom, C., Lipsitch, M. and Levin, B., Natural selection, infectious transfer and the existence conditions for bacterial plasmids, Genetics, 155, 1505–1519, 2000.
  • 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.
  • 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.
  • Whitman, A. and Ashrafiuon, H., Asymptotic theory of an infectious disease model, J. Math. Biol., 53, 287-304, 2006.
  • Lipsitch, M. and Levin, B., The population dynamics of antimicrobial chemotherapy, Antimicrob. Agents Ch., 41, 363–373, 1997.
  • 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.
  • Allen, L.J.S., An Introduction to Mathematical Biology, London: Pearson Education, 2007.
  • Hale, J. and Koçak, H., Dynamics and Bifurcations, New York: Springer-Verlag, 1991.
  • 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.
  • Antunes, L.C.S., Imperi, F., Carattoli, A. and Visca, P., Deciphering the Multifactorial Nature of Acinetobacter baumannii Pathogenicity, PLOSone, 6, 2011.
  • 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.
  • 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.
  • Pugliese, A. and Gandolfi, A., A simple model of pathogen–immune dynamics including specific and non-specific immunity, Math. Biosci., 214, 73–80, 2008.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
There are 32 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Bahatdin Daşbaşı

İlhan Öztürk

Publication Date August 15, 2018
Acceptance Date August 10, 2018
Published in Issue Year 2018 Volume: 10 Issue: 2

Cite

APA Daşbaşı, B., & Öztürk, İ. (2018). On The Stability Analysis of The General Mathematical Modeling of Bacterial Infection. International Journal of Engineering and Applied Sciences, 10(2), 93-117. https://doi.org/10.24107/ijeas.445520
AMA Daşbaşı B, Öztürk İ. On The Stability Analysis of The General Mathematical Modeling of Bacterial Infection. IJEAS. August 2018;10(2):93-117. doi:10.24107/ijeas.445520
Chicago Daşbaşı, Bahatdin, and İlhan Öztürk. “On The Stability Analysis of The General Mathematical Modeling of Bacterial Infection”. International Journal of Engineering and Applied Sciences 10, no. 2 (August 2018): 93-117. https://doi.org/10.24107/ijeas.445520.
EndNote Daşbaşı B, Öztürk İ (August 1, 2018) On The Stability Analysis of The General Mathematical Modeling of Bacterial Infection. International Journal of Engineering and Applied Sciences 10 2 93–117.
IEEE B. Daşbaşı and İ. Öztürk, “On The Stability Analysis of The General Mathematical Modeling of Bacterial Infection”, IJEAS, vol. 10, no. 2, pp. 93–117, 2018, doi: 10.24107/ijeas.445520.
ISNAD Daşbaşı, Bahatdin - Öztürk, İlhan. “On The Stability Analysis of The General Mathematical Modeling of Bacterial Infection”. International Journal of Engineering and Applied Sciences 10/2 (August 2018), 93-117. https://doi.org/10.24107/ijeas.445520.
JAMA Daşbaşı B, Öztürk İ. On The Stability Analysis of The General Mathematical Modeling of Bacterial Infection. IJEAS. 2018;10:93–117.
MLA Daşbaşı, Bahatdin and İlhan Öztürk. “On The Stability Analysis of The General Mathematical Modeling of Bacterial Infection”. International Journal of Engineering and Applied Sciences, vol. 10, no. 2, 2018, pp. 93-117, doi:10.24107/ijeas.445520.
Vancouver Daşbaşı B, Öztürk İ. On The Stability Analysis of The General Mathematical Modeling of Bacterial Infection. IJEAS. 2018;10(2):93-117.

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