Computational Mathematics and Mathematical Physics

, Volume 58, Issue 12, pp 1967–1976 | Cite as

Reaction–Diffusion Equations in Immunology

  • G. A. Bocharov
  • V. A. Volpert
  • A. L. TasevichEmail author


The paper is devoted to the recent works on reaction–diffusion models of virus infection dynamics in human and animal organisms. Various regimes of infection propagation in tissues are described. In particular, it is shown that infection can spread in tissues of organs as a reaction–diffusion wave. Methods for studying the conditions of the existence of wave modes of the time and space dynamics of infections is discussed.


virus infection immune response mathematical modeling reaction–diffusion equations time and space dynamics 



This work was supported by the Russian Foundation for Basic Research, project no. 17-01-00636; and by the Ministry for Education and Science of the Russian Federation within the program 5-100 for enhancing the competitiveness of the Peoples’ Friendship University of Russia among the leading science and education centers in 2016–2020.


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • G. A. Bocharov
    • 1
    • 2
  • V. A. Volpert
    • 1
    • 3
    • 4
    • 5
  • A. L. Tasevich
    • 1
    • 6
    Email author
  1. 1.Peoples’ Friendship University of RussiaMoscowRussia
  2. 2.Institute of Numerical Mathematics, Russian Academy of SciencesMoscowRussia
  3. 3.Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1VilleurbanneFrance
  4. 4.INRIA Team Dracula, INRIA Lyon La DouaVilleurbanneFrance
  5. 5.Poncelet Center, UMI 2615 CNRSMoscowRussia
  6. 6.Federal Research Center “Computer Science and Control,” Russian Academy of SciencesMoscowRussia

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