Mathematical Biosciences and Engineering, 2015, 12(5): 1007-1016. doi: 10.3934/mbe.2015.12.1007.

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

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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

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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Keywords viral dynamics; phenotype space; basicreproduction number.; Nowak--May model; singularly perturbed system; Darwinianfitness; variant space; HIV; slow-fast dynamics; viral evolution; integro--differential equations

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

References

  • 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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