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Mathematical Biosciences and Engineering

2015, Volume 12, Issue 5: 1007-1016. doi: 10.3934/mbe.2015.12.1007
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Order reduction for an RNA virus evolution model

  • 1.
    Centre de Recerca Matemática, Campus de Bellaterra, Edifici C, 08193 Barcelona
  • 2.
    Department of Applied Mathematics, Samara State Aerospace University (SSAU), 443086 Samara, 34, Moskovskoye shosse
  • 3.
    Department of Technical Cybernetics, Samara State Aerospace University (SSAU), 443086 Samara, 34, Moskovskoye shosse
  • Received: 01 August 2014 Accepted: 29 June 2018 Published: 01 June 2015

  • MSC : Primary: 92D15; Secondary: 35Q92, 34E13.

  • A mathematical or computational model in evolutionary biologyshould necessary combine several comparatively fast processes,which actually drive natural selection and evolution, with a veryslow process of evolution. As a result, several very differenttime scales are simultaneously present in the model; this makesits analytical study an extremely difficult task. However, thesignificant difference of the time scales implies the existence ofa possibility of the model order reduction through a process oftime separation. In this paper we conduct the procedure of modelorder reduction for a reasonably simple model of RNA virusevolution reducing the original system of three integro-partialderivative equations to a single equation. Computations confirmthat there is a good fit between the results for the original andreduced models.

    Citation: Andrei Korobeinikov, Aleksei Archibasov, Vladimir Sobolev. Order reduction for an RNA virus evolution model[J]. Mathematical Biosciences and Engineering, 2015, 12(5): 1007-1016. doi: 10.3934/mbe.2015.12.1007

    Related Papers:

  • A mathematical or computational model in evolutionary biologyshould necessary combine several comparatively fast processes,which actually drive natural selection and evolution, with a veryslow process of evolution. As a result, several very differenttime scales are simultaneously present in the model; this makesits analytical study an extremely difficult task. However, thesignificant difference of the time scales implies the existence ofa possibility of the model order reduction through a process oftime separation. In this paper we conduct the procedure of modelorder reduction for a reasonably simple model of RNA virusevolution reducing the original system of three integro-partialderivative equations to a single equation. Computations confirmthat there is a good fit between the results for the original andreduced models.


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    [1] Applicable Analysis, 91 (2012), 1265-1277.
    [2] Applicable Analysis, 52 (1994), 143-154.
    [3] Phil. Trans. R. Soc. B, 352 (1997), 11-20.
    [4] IEEE Trans. Aut. Control, 32 (1987), 260-263.
    [5] Bull. Math. Biol., 66 (2004), 879-883.
    [6] Math. Med. Biol., 26 (2009), 225-239.
    [7] Math. Med. Biol., 26 (2009), 309-321.
    [8] Math. Biosci. Eng., 11 (2014), 919-927.
    [9] Applicable Analysis, 89 (2010), 1271-1292.
    [10] SIAM, Philadelphia, 2005.
    [11] Computational Mathematics and Mathematical Physics, 47 (2007), 629-637.
    [12] Oxford University Press, New York, 2000.
    [13] J. Theor. Biol., 168 (1994), 291-308.
    [14] J. Mol. Evol, 51 (2000), 245-255.
    [15] J. Theor. Biol., 203 (2000), 285-301.
    [16] Phys. Rev. Lett., 76 (1996), 4440-4443.
    [17] Math. Med. Biol., 30 (2013), 65-72.
    [18] SIAM, Philadelphia, 1995.
    [19] TRENDS in Immunology, 23 (2002), 194-200.
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  • © 2015 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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