Stability analysis of pathogen-immune interaction dynamics

Akiko Murase, Toru Sasaki, Tsuyoshi Kajiwara

Research output: Contribution to journalArticlepeer-review

138 Citations (Scopus)


The paper considers models of dynamics of infectious disease in vivo from the standpoint of the mathematical analysis of stability. The models describe the interaction of the target cells, the pathogens, and the humoral immune response. The paper mainly focuses on the interior equilibrium, whose components are all positive. If the model ignores the absorption of the pathogens due to infection, the interior equilibrium is always asymptotically stable. On the other hand, if the model does consider it, the interior equilibrium can be unstable and a simple Hopf bifurcation can occur. A sufficient condition that the interior equilibrium is asymptotically stable is obtained. The condition explains that the interior equilibrium is asymptotically stable when experimental parameter values are used for the model. Moreover, the paper considers the models in which uninfected cells are involved in the immune response to pathogens, and are removed by the immune complexes. The effect of the involvement strongly affects the stability of the interior equilibria. The results are shown with the aid of symbolic calculation software.

Original languageEnglish
Pages (from-to)247-267
Number of pages21
JournalJournal of Mathematical Biology
Issue number3
Publication statusPublished - Sep 1 2005


  • Hopf bifurcation
  • Immune response, Stability
  • Infectious diseases
  • Symbolic calculation software

ASJC Scopus subject areas

  • Modelling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


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