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Reaction diffusion equations and the chronification of liver infections

Author

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  • Kerl, Hermann-Johannes
  • Langemann, Dirk
  • Vollrath, Antje

Abstract

A predator-prey system is used to model the time-dependent virus and lymphocyte population during a liver infection. We show mathematically that the resulting reaction-diffusion equation has non-trivial stationary solutions whenever the underlying domain is sufficiently large or fissured. The non-trivial stationary solutions are interpreted as chronic liver infections. Thus qualitative differences between acute and chronic hepatitis infections become dispensable. Finally, numerical simulations for the chronification are presented.

Suggested Citation

  • Kerl, Hermann-Johannes & Langemann, Dirk & Vollrath, Antje, 2012. "Reaction diffusion equations and the chronification of liver infections," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(11), pages 2145-2156.
    • Handle: RePEc:eee:matcom:v:82:y:2012:i:11:p:2145-2156
    DOI: 10.1016/j.matcom.2012.04.011
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    References listed on IDEAS

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    1. Stanca Ciupe & Anne Catlla & Jonathan Forde & David Schaeffer, 2011. "Dynamics of Hepatitis B Virus Infection: What Causes Viral Clearance?," Mathematical Population Studies, Taylor & Francis Journals, vol. 18(2), pages 87-105.
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