Open AccessConstruction of Lyapunov functions for some models of infectious diseases in vivo: From simple models to complex models
Author(s) -
Tsuyoshi Kajiwara,
Toru Sasaki,
Yasuhiro Takeuchi
Publication year - 2015
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2015.12.117
Subject(s) - lyapunov function , lyapunov redesign , lyapunov equation , constructive , mathematics , lyapunov optimization , computer science , nonlinear system , physics , process (computing) , quantum mechanics , operating system
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.