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Yıl 2021, Cilt: 17 Sayı: 4, 369 - 377, 29.12.2021

İlkem Turhan Çetinkaya Mehmet Kocabıyık Mevlüde Yakıt Ongun

Öz

Kaynakça

  • 1. Chen, CL, Tsai, HW, Wong, SS. 2010. Modeling the physiological glucose–insulin dynamic system on diabetics. Journal of Theoretical Biology; 265: 314–322.
  • 2. Dereouich, M, Boutayeb, A. 2002. The effect of physical exercise on the dynamics of glucose and insulin. Journal of Biomechanics; 35: 911–917.
  • 3. Neatpisarnvanit, C, Boston, JR. 2002. Estimation of Plasma Insulin From Plasma Glucose. IEEE Transactions on biomedical engineering, 49(11): 1253-1259.
  • 4. Li, J, Kuang,Y. Analysis of IVGTT glucose-insulin interaction models with time delay. 2001. Discrete and Continuous Dynamical Systems- Series B; 1(1): 103–124.
  • 5. Hussain, J, Zadeng, D. 2014. A mathematical model of glucose-insulin interaction. Science Vision; 14(2): 84-88.
  • 6. Wang, H, Li, J, Kuang, Y. 2007. Mathematical modeling and qualitative analysis of insulin therapies. Mathematical Biosciences; 210: 17–33.
  • 7. Al-Kahby, H, Dannan, F, Elaydi, S. Non-standard Discretization Methods for Some Biological Models. 2000. Applications of Nonstandard Finite Difference Schemes; 155-180.
  • 8. Mickens, RE. Difference Equations Theory and Applications, Atlanta, Ga, USA: Chapman & Hall, 1990.
  • 9. Mickens, RE. Advances in the applications of Nonstandard Finite Difference Schemes, Singapore: Wiley-Interscience, 2005.
  • 10. Mickens, RE. Nonstandard finite difference models of differential equations, World Scientific Publishing Co., Inc., River Edge, NJ, 1994.
  • 11. Mickens, RE. 2002. Nonstandard Finite Difference Schemes for Differential Equations. Journal of Difference Equations and Applications; 8(9): 823-847, DOI:10.1080/1023619021000000807.
  • 12. Mickens, RE. Exact solutions to a finite-difference model of a nonlinear reaction-advection equation: implications for numerical analysis. 1989. Numerical Methods for Partial Differential Equations; 5(4): 313-325.
  • 13. Arenas, AJ, Morano, JA, Cortes, JC. Non-standard numerical method for a mathematical model of RSV epidemiological transmission. 2008. Computers and Mathematics with Applications; 56: 670-678.
  • 14. Khalsaraei MM, Khodadosti, F. 2014. Nonstandard Finite Difference Schemes for Differential Equations, Sahand Communications in Mathematical Analysis; 1(2): 47-54.
  • 15. Yakıt Ongun, M, Turhan, İ. 2013. A Numerical Comparison for a Discrete HIV Infection of CD4+T-Cell Model Derived from Nontandard Numerical Scheme. Journal of Applied Mathematics; 2013.
  • 16. Yakıt Ongun, M, Arslan, D, Garrappa, R. 2013. Nonstandard finite difference schemes for a fractional-order Brusselator system. 2013. Advances in Difference Equations; 2013(102).
  • 17. Lombarte, M, Lupo, M, Campetelli, G, Basualdo, M, Rigalli, A. Mathematical model of glucose–insulin homeostasis in healthy rats. 2013. Mathematical Biosciences; 245: 269–277.
  • 18. Gopal, M. Digital Control Engineering, New Delhi: New Age International (P) Limited, Publishers, 2003.
  • 19. Gopal, M. Digital Control and State Variable Methods, Conventional and Intelligent Control Systems, New Delhi: Tata McGraw-Hill Publishing Company Limited, 2009.

Stability Analysis of Discretized Model of Glucose–Insulin Homeostasis

Yıl 2021, Cilt: 17 Sayı: 4, 369 - 377, 29.12.2021

İlkem Turhan Çetinkaya Mehmet Kocabıyık Mevlüde Yakıt Ongun

Öz

In this paper, the mathematical model which describes the glucose-insulin homeostasis in healthy rats is considered. The model is discretized by constructing a nonstandard finite difference (NSFD) scheme to obtain the numerical solutions. The equilibrium point of the discretized model is determined and stability analysis of the discretized model is discussed. The effect of time step sizes on 4th order Runge-Kutta method and NSFD method is presented. Also, comparison of NSFD scheme solution, Runge-Kutta-Fehlberg Method (RKF45) solution and analytical solution are presented in graphical form. The effectiveness of the proposed method in the solution and interpretation of the model is observed.
Keywords: Glucose-Insulin homeostasis, nonstandard finite difference scheme, stability analysis.

Anahtar Kelimeler

Glucose-Insulin homeostasis nonstandard finite difference scheme stability analysis

Kaynakça

  • 1. Chen, CL, Tsai, HW, Wong, SS. 2010. Modeling the physiological glucose–insulin dynamic system on diabetics. Journal of Theoretical Biology; 265: 314–322.
  • 2. Dereouich, M, Boutayeb, A. 2002. The effect of physical exercise on the dynamics of glucose and insulin. Journal of Biomechanics; 35: 911–917.
  • 3. Neatpisarnvanit, C, Boston, JR. 2002. Estimation of Plasma Insulin From Plasma Glucose. IEEE Transactions on biomedical engineering, 49(11): 1253-1259.
  • 4. Li, J, Kuang,Y. Analysis of IVGTT glucose-insulin interaction models with time delay. 2001. Discrete and Continuous Dynamical Systems- Series B; 1(1): 103–124.
  • 5. Hussain, J, Zadeng, D. 2014. A mathematical model of glucose-insulin interaction. Science Vision; 14(2): 84-88.
  • 6. Wang, H, Li, J, Kuang, Y. 2007. Mathematical modeling and qualitative analysis of insulin therapies. Mathematical Biosciences; 210: 17–33.
  • 7. Al-Kahby, H, Dannan, F, Elaydi, S. Non-standard Discretization Methods for Some Biological Models. 2000. Applications of Nonstandard Finite Difference Schemes; 155-180.
  • 8. Mickens, RE. Difference Equations Theory and Applications, Atlanta, Ga, USA: Chapman & Hall, 1990.
  • 9. Mickens, RE. Advances in the applications of Nonstandard Finite Difference Schemes, Singapore: Wiley-Interscience, 2005.
  • 10. Mickens, RE. Nonstandard finite difference models of differential equations, World Scientific Publishing Co., Inc., River Edge, NJ, 1994.
  • 11. Mickens, RE. 2002. Nonstandard Finite Difference Schemes for Differential Equations. Journal of Difference Equations and Applications; 8(9): 823-847, DOI:10.1080/1023619021000000807.
  • 12. Mickens, RE. Exact solutions to a finite-difference model of a nonlinear reaction-advection equation: implications for numerical analysis. 1989. Numerical Methods for Partial Differential Equations; 5(4): 313-325.
  • 13. Arenas, AJ, Morano, JA, Cortes, JC. Non-standard numerical method for a mathematical model of RSV epidemiological transmission. 2008. Computers and Mathematics with Applications; 56: 670-678.
  • 14. Khalsaraei MM, Khodadosti, F. 2014. Nonstandard Finite Difference Schemes for Differential Equations, Sahand Communications in Mathematical Analysis; 1(2): 47-54.
  • 15. Yakıt Ongun, M, Turhan, İ. 2013. A Numerical Comparison for a Discrete HIV Infection of CD4+T-Cell Model Derived from Nontandard Numerical Scheme. Journal of Applied Mathematics; 2013.
  • 16. Yakıt Ongun, M, Arslan, D, Garrappa, R. 2013. Nonstandard finite difference schemes for a fractional-order Brusselator system. 2013. Advances in Difference Equations; 2013(102).
  • 17. Lombarte, M, Lupo, M, Campetelli, G, Basualdo, M, Rigalli, A. Mathematical model of glucose–insulin homeostasis in healthy rats. 2013. Mathematical Biosciences; 245: 269–277.
  • 18. Gopal, M. Digital Control Engineering, New Delhi: New Age International (P) Limited, Publishers, 2003.
  • 19. Gopal, M. Digital Control and State Variable Methods, Conventional and Intelligent Control Systems, New Delhi: Tata McGraw-Hill Publishing Company Limited, 2009.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

İlkem Turhan Çetinkaya 0000-0002-5520-310X

Mehmet Kocabıyık 0000-0002-7701-6946

Mevlüde Yakıt Ongun 0000-0003-2363-9395

Yayımlanma Tarihi 29 Aralık 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 17 Sayı: 4

Kaynak Göster

APA Turhan Çetinkaya, İ., Kocabıyık, M., & Yakıt Ongun, M. (2021). Stability Analysis of Discretized Model of Glucose–Insulin Homeostasis. Celal Bayar University Journal of Science, 17(4), 369-377.
AMA Turhan Çetinkaya İ, Kocabıyık M, Yakıt Ongun M. Stability Analysis of Discretized Model of Glucose–Insulin Homeostasis. CBUJOS. Aralık 2021;17(4):369-377.
Chicago Turhan Çetinkaya, İlkem, Mehmet Kocabıyık, ve Mevlüde Yakıt Ongun. “Stability Analysis of Discretized Model of Glucose–Insulin Homeostasis”. Celal Bayar University Journal of Science 17, sy. 4 (Aralık 2021): 369-77.
EndNote Turhan Çetinkaya İ, Kocabıyık M, Yakıt Ongun M (01 Aralık 2021) Stability Analysis of Discretized Model of Glucose–Insulin Homeostasis. Celal Bayar University Journal of Science 17 4 369–377.
IEEE İ. Turhan Çetinkaya, M. Kocabıyık, ve M. Yakıt Ongun, “Stability Analysis of Discretized Model of Glucose–Insulin Homeostasis”, CBUJOS, c. 17, sy. 4, ss. 369–377, 2021.
ISNAD Turhan Çetinkaya, İlkem vd. “Stability Analysis of Discretized Model of Glucose–Insulin Homeostasis”. Celal Bayar University Journal of Science 17/4 (Aralık 2021), 369-377.
JAMA Turhan Çetinkaya İ, Kocabıyık M, Yakıt Ongun M. Stability Analysis of Discretized Model of Glucose–Insulin Homeostasis. CBUJOS. 2021;17:369–377.
MLA Turhan Çetinkaya, İlkem vd. “Stability Analysis of Discretized Model of Glucose–Insulin Homeostasis”. Celal Bayar University Journal of Science, c. 17, sy. 4, 2021, ss. 369-77.
Vancouver Turhan Çetinkaya İ, Kocabıyık M, Yakıt Ongun M. Stability Analysis of Discretized Model of Glucose–Insulin Homeostasis. CBUJOS. 2021;17(4):369-77.
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