Lyapunov functionals for multistrain models with infinite delay

Yoji Otani; Tsuyoshi Kajiwara; Toru Sasaki

doi:10.3934/dcdsb.2017025

Lyapunov functionals for multistrain models with infinite delay

Yoji Otani, Tsuyoshi Kajiwara, Toru Sasaki

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We construct Lyapunov functionals for delay differential equation models of infectious diseases in vivo to analyze the stability of the equilibria. The Lyapunov functionals contain the terms that integrate over all previous states. An appropriate evaluation of the logarithm functions in those terms guarantees the existence of the integrals. We apply the rigorous analysis for the one-strain models to multistrain models by using mathematical induction.

Original language	English
Pages (from-to)	507-536
Number of pages	30
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	22
Issue number	2
DOIs	https://doi.org/10.3934/dcdsb.2017025
Publication status	Published - Mar 2017

Keywords

Delay differential equation
Global stability
Infinitely distributed delay
Lyapunov functional
Multistrain
Virus-immune model

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.3934/dcdsb.2017025

Cite this

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abstract = "We construct Lyapunov functionals for delay differential equation models of infectious diseases in vivo to analyze the stability of the equilibria. The Lyapunov functionals contain the terms that integrate over all previous states. An appropriate evaluation of the logarithm functions in those terms guarantees the existence of the integrals. We apply the rigorous analysis for the one-strain models to multistrain models by using mathematical induction.",

keywords = "Delay differential equation, Global stability, Infinitely distributed delay, Lyapunov functional, Multistrain, Virus-immune model",

author = "Yoji Otani and Tsuyoshi Kajiwara and Toru Sasaki",

year = "2017",

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T1 - Lyapunov functionals for multistrain models with infinite delay

AU - Otani, Yoji

AU - Kajiwara, Tsuyoshi

AU - Sasaki, Toru

PY - 2017/3

Y1 - 2017/3

N2 - We construct Lyapunov functionals for delay differential equation models of infectious diseases in vivo to analyze the stability of the equilibria. The Lyapunov functionals contain the terms that integrate over all previous states. An appropriate evaluation of the logarithm functions in those terms guarantees the existence of the integrals. We apply the rigorous analysis for the one-strain models to multistrain models by using mathematical induction.

AB - We construct Lyapunov functionals for delay differential equation models of infectious diseases in vivo to analyze the stability of the equilibria. The Lyapunov functionals contain the terms that integrate over all previous states. An appropriate evaluation of the logarithm functions in those terms guarantees the existence of the integrals. We apply the rigorous analysis for the one-strain models to multistrain models by using mathematical induction.

KW - Delay differential equation

KW - Global stability

KW - Infinitely distributed delay

KW - Lyapunov functional

KW - Multistrain

KW - Virus-immune model

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JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 2

ER -

Lyapunov functionals for multistrain models with infinite delay

Abstract

Keywords

ASJC Scopus subject areas

UN SDGs

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