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Fractional-order Mathematical Modeling of Bacterial Competition with Theraphy of Multiple Antibiotics

Yıl 2019, Sayı: 26, 90 - 103, 01.01.2019

Bahatdin Daşbaşı

Öz

In this study, a
mathematical model in form fractional-order differential equations (FDE) system
identifying population dynamics in two species bacteria struggling one another
and exposed to multiple antibiotics simultaneously, was suggested. Stability
analysis of the equilibrium points of the proposed model was also carried out.
Additionally, the results of the analysis have promoted by numerical simulations.

Anahtar Kelimeler

Fractional-order differential equation Stability analysis Numerical simulation

Kaynakça

  • [1] H. El-Saka and A. El-Sayed, Fractional Order Equations and Dynamical Systems. Germany: Lambrt Academic Publishing, 2013.
  • [2] B. Daşbaşı, The Fractional-Order mathematical modeling of bacterial resistance against multiple antibiotics in case of local bacterial infection, Sakarya University Journal of Science 251 (2017) 1-13.
  • [3] T. J. Faber, A. Jaishankar, and G. H. McKinley, Describing the firmness, springiness and rubberiness of food gels using fractional calculus. Part II: Measurements on semi-hard cheese, Food Hydrocolloids 62 (2017) 325-339.
  • [4] C.-Q. Fang, H.-Y. Sun, and J.-P. Gu, Application of Fractional Calculus Methods to Viscoelastic Response of Amorphous Shape Memory Polymers, Journal of Mechanics 4 (2015) 427-432.
  • [5] J. F. Gomez-Aguilar, R. Razo-Hernandez, and D. Granados-Lieberman, A physical interpretation of fractional calculus in observables terms: analysis of the fractional time constant and the transitory response, Revista Mexicana de Fisica 60 (2014) 32–38.
  • [6] C. Ionescu, R. Caponetto, and Y.-Q. Chen, Special Issue on Fractional Order Modeling and Control in Mechatronics, Mechatronics 23 (2013) 739-740.
  • [7] Y. Liu, Y.-F. Pu, X.-D. Shen, and J.-L. Zhou, Design of 1/2 n order analog fractance approximation circuit based on continued fractions decomposition, Journal of Circuits, Systems and Computers 44 (2012) 153-158.
  • [8] B. Daşbaşı, İ. Öztürk, and F. Özköse, Mathematical Modelling of Bacterial Competition with Multiple Antibiotics and it's Stability Analysis, Karaelmas Fen ve Mühendislik Dergisi 6 (2016) 299-306.
  • [9] K. M. Owolabi, Riemann-Liouville Fractional Derivative and Application to Model Chaotic Differential Equations, Progr. Fract. Differ. Appl. 4 (2018) 99-110.
  • [10] E. I. Mondragón et al., Mathematical modeling on bacterial resistance to multiple antibiotics caused by spontaneous mutations, BioSystems 117 (2014) 60–67.
  • [11] M. M. Khader, The Modeling Dynamics of HIV and CD4+ T-cells During Primary Infection in Fractional Order: Numerical Simulation, Mediterr. J. Math. 15 (2018) 1-17.
  • [12] L. C. S. Antunes, F. Imperi, A. Carattoli, and P. Visca, Deciphering the Multifactorial Nature of Acinetobacter baumannii Pathogenicity, PLOSone 6 (2011).
  • [13] M. D. Carruthers, P. A. Nicholson, E. N. Tracy, and R. S. Munson, Acinetobacter baumannii Utilizes a Type VI Secretion System for Bacterial Competition, PLOSone 8 (2013).
  • [14] H. Fujikawa, A. Kai, and S. Morozumi, A new logistic model for Escherichia coli growth at constant and dynamic temperatures, Food Microbiol. 21 (2004) 501–509.
  • [15] D. Gur et al., Antimicrobial resistance in gram-negative hospital isolates: results of the Turkish HITIT-2 Surveillance Study of 2007, J. Chem. 21 (2009) 383-389.
  • [16] A. Hadadi et al., Antimicrobial resistance patterns among Gram-negative bacilli isolated from patients with nosocomial infections: Disk diffusion versus E-test, Tehran Univ. Med. J. 65 (2007) 1-10.
  • [17] S. H. MacVane, J. L. Kuti, and D. P. Nicolau, Prolonging B-lactam infusion: A review of the rationale and evidence, and guidance for implementation, Int. J. of Antimic. Ag. 43 (2014) 105-113.
  • [18] A. F. Syed-Mohamed, Pharmacokinetic and Pharmacodynamic Modeling of Antibiotics and Bacterial Drug Resistance., Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Pharmacy 170 (2013).

Yıl 2019, Sayı: 26, 90 - 103, 01.01.2019

Bahatdin Daşbaşı

Öz

Kaynakça

  • [1] H. El-Saka and A. El-Sayed, Fractional Order Equations and Dynamical Systems. Germany: Lambrt Academic Publishing, 2013.
  • [2] B. Daşbaşı, The Fractional-Order mathematical modeling of bacterial resistance against multiple antibiotics in case of local bacterial infection, Sakarya University Journal of Science 251 (2017) 1-13.
  • [3] T. J. Faber, A. Jaishankar, and G. H. McKinley, Describing the firmness, springiness and rubberiness of food gels using fractional calculus. Part II: Measurements on semi-hard cheese, Food Hydrocolloids 62 (2017) 325-339.
  • [4] C.-Q. Fang, H.-Y. Sun, and J.-P. Gu, Application of Fractional Calculus Methods to Viscoelastic Response of Amorphous Shape Memory Polymers, Journal of Mechanics 4 (2015) 427-432.
  • [5] J. F. Gomez-Aguilar, R. Razo-Hernandez, and D. Granados-Lieberman, A physical interpretation of fractional calculus in observables terms: analysis of the fractional time constant and the transitory response, Revista Mexicana de Fisica 60 (2014) 32–38.
  • [6] C. Ionescu, R. Caponetto, and Y.-Q. Chen, Special Issue on Fractional Order Modeling and Control in Mechatronics, Mechatronics 23 (2013) 739-740.
  • [7] Y. Liu, Y.-F. Pu, X.-D. Shen, and J.-L. Zhou, Design of 1/2 n order analog fractance approximation circuit based on continued fractions decomposition, Journal of Circuits, Systems and Computers 44 (2012) 153-158.
  • [8] B. Daşbaşı, İ. Öztürk, and F. Özköse, Mathematical Modelling of Bacterial Competition with Multiple Antibiotics and it's Stability Analysis, Karaelmas Fen ve Mühendislik Dergisi 6 (2016) 299-306.
  • [9] K. M. Owolabi, Riemann-Liouville Fractional Derivative and Application to Model Chaotic Differential Equations, Progr. Fract. Differ. Appl. 4 (2018) 99-110.
  • [10] E. I. Mondragón et al., Mathematical modeling on bacterial resistance to multiple antibiotics caused by spontaneous mutations, BioSystems 117 (2014) 60–67.
  • [11] M. M. Khader, The Modeling Dynamics of HIV and CD4+ T-cells During Primary Infection in Fractional Order: Numerical Simulation, Mediterr. J. Math. 15 (2018) 1-17.
  • [12] L. C. S. Antunes, F. Imperi, A. Carattoli, and P. Visca, Deciphering the Multifactorial Nature of Acinetobacter baumannii Pathogenicity, PLOSone 6 (2011).
  • [13] M. D. Carruthers, P. A. Nicholson, E. N. Tracy, and R. S. Munson, Acinetobacter baumannii Utilizes a Type VI Secretion System for Bacterial Competition, PLOSone 8 (2013).
  • [14] H. Fujikawa, A. Kai, and S. Morozumi, A new logistic model for Escherichia coli growth at constant and dynamic temperatures, Food Microbiol. 21 (2004) 501–509.
  • [15] D. Gur et al., Antimicrobial resistance in gram-negative hospital isolates: results of the Turkish HITIT-2 Surveillance Study of 2007, J. Chem. 21 (2009) 383-389.
  • [16] A. Hadadi et al., Antimicrobial resistance patterns among Gram-negative bacilli isolated from patients with nosocomial infections: Disk diffusion versus E-test, Tehran Univ. Med. J. 65 (2007) 1-10.
  • [17] S. H. MacVane, J. L. Kuti, and D. P. Nicolau, Prolonging B-lactam infusion: A review of the rationale and evidence, and guidance for implementation, Int. J. of Antimic. Ag. 43 (2014) 105-113.
  • [18] A. F. Syed-Mohamed, Pharmacokinetic and Pharmacodynamic Modeling of Antibiotics and Bacterial Drug Resistance., Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Pharmacy 170 (2013).
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Araştırma Makalesi
Yazarlar

Bahatdin Daşbaşı 0000-0001-8201-7495

Yayımlanma Tarihi 1 Ocak 2019
Gönderilme Tarihi 27 Temmuz 2018
Yayımlandığı Sayı Yıl 2019 Sayı: 26

Kaynak Göster

APA Daşbaşı, B. (2019). Fractional-order Mathematical Modeling of Bacterial Competition with Theraphy of Multiple Antibiotics. Journal of New Theory(26), 90-103.
AMA Daşbaşı B. Fractional-order Mathematical Modeling of Bacterial Competition with Theraphy of Multiple Antibiotics. JNT. Ocak 2019;(26):90-103.
Chicago Daşbaşı, Bahatdin. “Fractional-Order Mathematical Modeling of Bacterial Competition With Theraphy of Multiple Antibiotics”. Journal of New Theory, sy. 26 (Ocak 2019): 90-103.
EndNote Daşbaşı B (01 Ocak 2019) Fractional-order Mathematical Modeling of Bacterial Competition with Theraphy of Multiple Antibiotics. Journal of New Theory 26 90–103.
IEEE B. Daşbaşı, “Fractional-order Mathematical Modeling of Bacterial Competition with Theraphy of Multiple Antibiotics”, JNT, sy. 26, ss. 90–103, Ocak 2019.
ISNAD Daşbaşı, Bahatdin. “Fractional-Order Mathematical Modeling of Bacterial Competition With Theraphy of Multiple Antibiotics”. Journal of New Theory 26 (Ocak 2019), 90-103.
JAMA Daşbaşı B. Fractional-order Mathematical Modeling of Bacterial Competition with Theraphy of Multiple Antibiotics. JNT. 2019;:90–103.
MLA Daşbaşı, Bahatdin. “Fractional-Order Mathematical Modeling of Bacterial Competition With Theraphy of Multiple Antibiotics”. Journal of New Theory, sy. 26, 2019, ss. 90-103.
Vancouver Daşbaşı B. Fractional-order Mathematical Modeling of Bacterial Competition with Theraphy of Multiple Antibiotics. JNT. 2019(26):90-103.
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