Construction of Lyapunov functions for some models of infectious diseases in vivo: From simple models to complex models

Tsuyoshi Kajiwara, Toru Sasaki, Yasuhiro Takeuchi

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We present a constructive method for Lyapunov functions for ordinary differential equation models of infectious diseases in vivo. We consider models derived from the Nowak-Bangham models. We construct Lyapunov functions for complex models using those of simpler models. Especially, we construct Lyapunov functions for models with an immune variable from those for models without an immune variable, a Lyapunov functions of a model with absorption effect from that for a model without absorption effect. We make the construction clear for Lyapunov functions proposed previously, and present new results with our method.

Original languageEnglish
Pages (from-to)117-133
Number of pages17
JournalMathematical Biosciences and Engineering
Volume12
Issue number1
DOIs
Publication statusPublished - Feb 1 2015

Keywords

  • Immunity
  • Infectious diseases
  • Lyapunov functions
  • Ordinary differential equations
  • Stability

ASJC Scopus subject areas

  • Modelling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics

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