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Hanta Virüs Modelinden Elde Edilen Fisher-Kolmogorov Denkleminin Lie Simetri Analizi

Year 2018, Volume: 22 Issue: 2, 754 - 759, 15.08.2018

Mehmet Kocabıyık Mevlüde Yakıt Ongun

Abstract

Bu makalede, kısmi diferansiyel denklem kullanılarak modellenen bir epidemik model çalışılmıştır. Hanta virüs modeli de denilen bu modelde tüm fare popülasyonu Ms ve Mi olarak iki sınıfa ayrılmıştır.  M= Ms + Mi şeklinde toplam fare popülasyonunu veren, Fisher-Kolmogorov kısmi diferansiyel denkleminin genel çözümü için Lie simetri analizinden faydalanılmıştır.

Keywords

Hanta virüs model Fisher-Kolmogorov denklemi; Reaksiyon-Difüzyon denklemi; Lie simetri metodu

References

  • [1] Abramson, G., and Kenkre, V. M. 2002. Spatiotemporal Patterns in the Hantavirus Infection. Physical Review E, 66.1, 011912.
  • [2] Abramson, G., Kenkre, V. M., Yates, T. L., Parmenter, R. R. 2003. Traveling Waves of Infection in the Hantavirus Epidemics. Bulletin of mathematical biology, 65(3), 519-534 .
  • [3] Allen, L. JS., Michel, L., and Carleton J. P. 2003. The Dynamics of Two Viral Infections in a Single Host Population with Applications to Hantavirus. Mathematical biosciences 186.2, 191-21 .
  • [4] Chen, M., Clemence, D. P. 2006. Analysis of and Numerical Schemes for a Mouse Population Model in Hantavirus Epidemics. Journal of Difference Equations and Applications, 12(9), 887-899 .
  • [5] Allen, L. JS., Robert K. M., Colleen B. J. 2006. Mathematical Models for Hantavirus Infection in Rodents. Bulletin of mathematical biology 68.3, 511-524.
  • [6] Rida, S. Z., El Radi, A. A., Arafa, A., Khalil, M. 2012. The Effect of the Environmental Parameter on the Hantavirus Infection through a Fractional-order SI model. International Journal of Basic and Applied Sciences, 1(2), 88-99.
  • [7] Ruan, S., Jianhong W. 2009. Modeling spatial Spread of Communicable Diseases Involving Animal Hosts. Spatial ecology, 293-316.
  • [8] Karadem, Z.G., Ongun, M.Y.. 2016. Logistic Differential Equation Obtained from Hanta-virus Model. Suleyman Demirel University Journal of Science (e-Journal), 11(1), 82-91.
  • [9] Bluman G.W., Kumei S. 1989. Symmetries and Differential Equations. New York, Springer-Verlag.
  • [10] Cohen, A., 1911. An Inroduction To The Lie Theory Of One-Parameter Groups With Applications To The Solutions Of Differantial Equations. D.C. Heath Co., Publishers,Boston, New York, Chicago.
  • [11] Ibragimov, N. H. 2001. Selected Works. Vol. 1, 2. Karlskrona, Sweden: Alga Publications, Blekinge Institute of Technology.
  • [12] Oliver, P.J. 1986. Applications of Lie Groups to Differential Equations, Springer-Verlag, New York.
  • [13] Ovsiannikov, L.V., 1982. Group Analysis of Differential Equations. Academic Press, New York.
  • [14] Page, J.M. 1897. Ordinary Differantial Equations An Elementary Text Book With in Introduction To Lie's Theory Of The Group Of One Parameter. Macmillan And Co. Limited, London.
  • [15] Bluman, G. W., Stephen C. A. 2002. Symmetry and Integration Methods for Differential Equations. No. 154, Springer, Verlag New York,Inc.
  • [16] Hyden, P.E, 2000. Symmetry Methods for Differential Equations (A Beginner's Guide). Cambridge Texts In Applied Mathematics.
  • [17] Clarksonz, P. A., Elizabeth, L. M. 1994. Symmetry Reductions and Exact Solutions of a Class of Nonlinear Heat Equations. Physica D: Nonlinear Phenomena 70.3, 250-288.
  • [18] Gbetoula, M.F.K. 2011. Symmetry Analysis of Fisher’s Equation. University of KwaZulu-Natal, South Africa, 3-21 .
  • [19] Verna, A., Ram, J., Mehmet, K. 2014. Analytic and Numerical Solutions of Nonlinear Diffusion Equations Via Symmetry Reductions. Advances in Difference Equations (2014), (1-13).
  • [20] Mohamed, Y.F. 2015. Mathematical Modeling Of The Spread Of Hantavirus Infection. Diss, Universiti Sains, Malaysia. Anthony Z. 1979. "Explicit solutions of Fisher's equation for a special wave speed." Bulletin of Mathematical Biology 41.6 :835-840.
  • [21] Kaushal, R. S., Ranjit K., and Awadhesh P. 2006. "On the exact solutions of nonlinear diffusion-reaction equations with quadratic and cubic nonlinearities."Pramana 67.2, 249-256.
  • [22] Ablowitz, M. J., and Anthony Z. 1979. Explicit Solutions of Fisher's Equation for a Special Wave Speed. Bulletin of Mathematical Biology, 41.6 :835-840.
  • [23] Kaushal, R. S., Ranjit, K., Awadhesh, P. 2006. On the Exact Solutions of Nonlinear Diffusion-Reaction Equations with Quadratic and Cubic Nonlinearities. Pramana, 67.2, 249-256.

Year 2018, Volume: 22 Issue: 2, 754 - 759, 15.08.2018

Mehmet Kocabıyık Mevlüde Yakıt Ongun

Abstract

References

  • [1] Abramson, G., and Kenkre, V. M. 2002. Spatiotemporal Patterns in the Hantavirus Infection. Physical Review E, 66.1, 011912.
  • [2] Abramson, G., Kenkre, V. M., Yates, T. L., Parmenter, R. R. 2003. Traveling Waves of Infection in the Hantavirus Epidemics. Bulletin of mathematical biology, 65(3), 519-534 .
  • [3] Allen, L. JS., Michel, L., and Carleton J. P. 2003. The Dynamics of Two Viral Infections in a Single Host Population with Applications to Hantavirus. Mathematical biosciences 186.2, 191-21 .
  • [4] Chen, M., Clemence, D. P. 2006. Analysis of and Numerical Schemes for a Mouse Population Model in Hantavirus Epidemics. Journal of Difference Equations and Applications, 12(9), 887-899 .
  • [5] Allen, L. JS., Robert K. M., Colleen B. J. 2006. Mathematical Models for Hantavirus Infection in Rodents. Bulletin of mathematical biology 68.3, 511-524.
  • [6] Rida, S. Z., El Radi, A. A., Arafa, A., Khalil, M. 2012. The Effect of the Environmental Parameter on the Hantavirus Infection through a Fractional-order SI model. International Journal of Basic and Applied Sciences, 1(2), 88-99.
  • [7] Ruan, S., Jianhong W. 2009. Modeling spatial Spread of Communicable Diseases Involving Animal Hosts. Spatial ecology, 293-316.
  • [8] Karadem, Z.G., Ongun, M.Y.. 2016. Logistic Differential Equation Obtained from Hanta-virus Model. Suleyman Demirel University Journal of Science (e-Journal), 11(1), 82-91.
  • [9] Bluman G.W., Kumei S. 1989. Symmetries and Differential Equations. New York, Springer-Verlag.
  • [10] Cohen, A., 1911. An Inroduction To The Lie Theory Of One-Parameter Groups With Applications To The Solutions Of Differantial Equations. D.C. Heath Co., Publishers,Boston, New York, Chicago.
  • [11] Ibragimov, N. H. 2001. Selected Works. Vol. 1, 2. Karlskrona, Sweden: Alga Publications, Blekinge Institute of Technology.
  • [12] Oliver, P.J. 1986. Applications of Lie Groups to Differential Equations, Springer-Verlag, New York.
  • [13] Ovsiannikov, L.V., 1982. Group Analysis of Differential Equations. Academic Press, New York.
  • [14] Page, J.M. 1897. Ordinary Differantial Equations An Elementary Text Book With in Introduction To Lie's Theory Of The Group Of One Parameter. Macmillan And Co. Limited, London.
  • [15] Bluman, G. W., Stephen C. A. 2002. Symmetry and Integration Methods for Differential Equations. No. 154, Springer, Verlag New York,Inc.
  • [16] Hyden, P.E, 2000. Symmetry Methods for Differential Equations (A Beginner's Guide). Cambridge Texts In Applied Mathematics.
  • [17] Clarksonz, P. A., Elizabeth, L. M. 1994. Symmetry Reductions and Exact Solutions of a Class of Nonlinear Heat Equations. Physica D: Nonlinear Phenomena 70.3, 250-288.
  • [18] Gbetoula, M.F.K. 2011. Symmetry Analysis of Fisher’s Equation. University of KwaZulu-Natal, South Africa, 3-21 .
  • [19] Verna, A., Ram, J., Mehmet, K. 2014. Analytic and Numerical Solutions of Nonlinear Diffusion Equations Via Symmetry Reductions. Advances in Difference Equations (2014), (1-13).
  • [20] Mohamed, Y.F. 2015. Mathematical Modeling Of The Spread Of Hantavirus Infection. Diss, Universiti Sains, Malaysia. Anthony Z. 1979. "Explicit solutions of Fisher's equation for a special wave speed." Bulletin of Mathematical Biology 41.6 :835-840.
  • [21] Kaushal, R. S., Ranjit K., and Awadhesh P. 2006. "On the exact solutions of nonlinear diffusion-reaction equations with quadratic and cubic nonlinearities."Pramana 67.2, 249-256.
  • [22] Ablowitz, M. J., and Anthony Z. 1979. Explicit Solutions of Fisher's Equation for a Special Wave Speed. Bulletin of Mathematical Biology, 41.6 :835-840.
  • [23] Kaushal, R. S., Ranjit, K., Awadhesh, P. 2006. On the Exact Solutions of Nonlinear Diffusion-Reaction Equations with Quadratic and Cubic Nonlinearities. Pramana, 67.2, 249-256.
There are 23 citations in total.

Details

Journal Section Articles
Authors

Mehmet Kocabıyık

Mevlüde Yakıt Ongun

Publication Date August 15, 2018
Published in Issue Year 2018 Volume: 22 Issue: 2

Cite

APA Kocabıyık, M., & Yakıt Ongun, M. (2018). Hanta Virüs Modelinden Elde Edilen Fisher-Kolmogorov Denkleminin Lie Simetri Analizi. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22(2), 754-759. https://doi.org/10.19113/sdufbed.41518
AMA Kocabıyık M, Yakıt Ongun M. Hanta Virüs Modelinden Elde Edilen Fisher-Kolmogorov Denkleminin Lie Simetri Analizi. SDÜ Fen Bil Enst Der. August 2018;22(2):754-759. doi:10.19113/sdufbed.41518
Chicago Kocabıyık, Mehmet, and Mevlüde Yakıt Ongun. “Hanta Virüs Modelinden Elde Edilen Fisher-Kolmogorov Denkleminin Lie Simetri Analizi”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22, no. 2 (August 2018): 754-59. https://doi.org/10.19113/sdufbed.41518.
EndNote Kocabıyık M, Yakıt Ongun M (August 1, 2018) Hanta Virüs Modelinden Elde Edilen Fisher-Kolmogorov Denkleminin Lie Simetri Analizi. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 2 754–759.
IEEE M. Kocabıyık and M. Yakıt Ongun, “Hanta Virüs Modelinden Elde Edilen Fisher-Kolmogorov Denkleminin Lie Simetri Analizi”, SDÜ Fen Bil Enst Der, vol. 22, no. 2, pp. 754–759, 2018, doi: 10.19113/sdufbed.41518.
ISNAD Kocabıyık, Mehmet - Yakıt Ongun, Mevlüde. “Hanta Virüs Modelinden Elde Edilen Fisher-Kolmogorov Denkleminin Lie Simetri Analizi”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22/2 (August 2018), 754-759. https://doi.org/10.19113/sdufbed.41518.
JAMA Kocabıyık M, Yakıt Ongun M. Hanta Virüs Modelinden Elde Edilen Fisher-Kolmogorov Denkleminin Lie Simetri Analizi. SDÜ Fen Bil Enst Der. 2018;22:754–759.
MLA Kocabıyık, Mehmet and Mevlüde Yakıt Ongun. “Hanta Virüs Modelinden Elde Edilen Fisher-Kolmogorov Denkleminin Lie Simetri Analizi”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 22, no. 2, 2018, pp. 754-9, doi:10.19113/sdufbed.41518.
Vancouver Kocabıyık M, Yakıt Ongun M. Hanta Virüs Modelinden Elde Edilen Fisher-Kolmogorov Denkleminin Lie Simetri Analizi. SDÜ Fen Bil Enst Der. 2018;22(2):754-9.
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