Bulletin of Mathematical Biology

, Volume 81, Issue 11, pp 4743–4760 | Cite as

Modeling the Chronification Tendency of Liver Infections as Evolutionary Advantage

  • Cordula ReischEmail author
  • Dirk Langemann
Special Issue: Modelling Biological Evolution: Developing Novel Approaches


Here, we discuss how the tendency of a liver infection to chronify can be seen as an evolutionary advantage for infected individuals. For this purpose, we present a set of reaction–diffusion equations as a mathematical model of viral liver infections, which allows chronic and acute courses of the liver infection. We introduce a cumulative wealth function, and finally, we show that an immune response favoring the chronification is evolutionary advantageous at the same time.


Reaction–diffusion equations Evolutionary advantage Property forming Liver inflammation Mathematical modeling 



  1. Aston P (2018) A new model for the dynamics of hepatitis C infection: derivation, analysis and implications. Viruses 10(4):195CrossRefGoogle Scholar
  2. Bowen DG, Walker CM (2005) Adaptive immune response in acute and chronic hepatitis C virus infection. Nature 436(7053):946–952CrossRefGoogle Scholar
  3. Darai G (2012) Lexikon der Infektionskrankheiten der Menschen. Springer, BerlinCrossRefGoogle Scholar
  4. Frank SA (1991) Ecological and genetic models of host-pathogen coevolution. Heredity 67:73–83CrossRefGoogle Scholar
  5. Graw F, Balagopal A, Kandathil AJ, Ray SC, Thomas DL, Ribeiro RM, Perelson AS (2014) Inferring viral dynamics in chronically HCV infected patients from the spatial distribution of infected hepatocytes. PLoS Comput Biol 10(11):e1003934CrossRefGoogle Scholar
  6. Hastings A, Abbott KC, Cuddington K, Francis T, Gellner G, Lai Y-C, Morozov A, Petrovskii S, Scranton K, Zeeman ML (2018) Transient phenomena in ecology. Science 361(990):eaat6412CrossRefGoogle Scholar
  7. Hattaf K, Yousfi N (2015) A generalized HBV model with diffusion and two delays. Comput Math Appl 69:31–40MathSciNetCrossRefGoogle Scholar
  8. Kanel GC (2017) Pathology of liver diseases. Wiley, HobokenCrossRefGoogle Scholar
  9. Kerl H-J, Langemann D, Vollrath A (2012) Reaction–diffusion equations and the chronification of liver infections. Math Comput Simul 82:2145–2156MathSciNetCrossRefGoogle Scholar
  10. Langemann D, Reisch C (2018) Chemotactic effects in reaction–diffusion equations for inflammations. J Biol Phys (under review)Google Scholar
  11. Murray JD (2002) Mathematical biology I/II. Springer, New YorkCrossRefGoogle Scholar
  12. Rehermann B, Nascimbeni M (2005) Immunology of hepatitis B virus and hepatitis C virus infection. Nat Rev Immunol 5:215–229CrossRefGoogle Scholar
  13. Reisch C, Schroth I (2018) Hierarchies of modeling infections: comparison of reaction–diffusion system and cellular automaton. In: ARGESIM Report, Proceedings of MathMod2018, vol 55. Wien, pp 49–50Google Scholar
  14. Richter O, Söndgerath S (1990) Parameter estimation in ecology: the link between data and models. VCH, WeinheimzbMATHGoogle Scholar
  15. Roselius L, Langemann D, Müller J, Hense BA, Filges S, Jahn D, Münch R (2014) Modelling and analysis of a gene-regulatory feed-forward loop with basal expression of the second regulator. J Theor Biol 363C:290–299MathSciNetCrossRefGoogle Scholar
  16. Rosenzweig ML, MacArthur RH (1963) Graphical representation and stability conditions of predator–prey interactions. Am Nat 97(895):209–223CrossRefGoogle Scholar
  17. Scheuer P, Lewkowitch JH (2000) Liver biopsy interpretations. W. B. Saunders, LondonGoogle Scholar
  18. Smoller J (1983) Shock waves and reaction–diffusion equations. Springer, New YorkCrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2019

Authors and Affiliations

  1. 1.Institute of Computational Mathematics, AG PDETU BraunschweigBraunschweigGermany

Personalised recommendations