Mehmet KOCABIYIK, Mevlüde YAKIT ONGUN

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

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.

Anahtar Kelimeler:

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

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[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.