Global stability of an age-structured model for pathogen–immune interaction

Research output: Contribution to journalArticle

Abstract

In this paper, we present an age-structured mathematical model for infectious disease in vivo with infection age of cells. The model contains an immune variable and the effect of absorption of pathogens into uninfected cells. We construct Lyapunov functionals for the model and prove that the time derivative of the functionals are nonpositive. Using this, we prove the global stability results for the model. Especially, we present the full mathematical detail of the proof of the global stability.

Original languageEnglish
Pages (from-to)1-30
Number of pages30
JournalJournal of Applied Mathematics and Computing
DOIs
Publication statusAccepted/In press - Jun 5 2018

Fingerprint

Age-structured Model
Global Stability
Interaction
Lyapunov Functionals
Cell
Infectious Diseases
Pathogens
Infection
Absorption
Model
Mathematical Model
Mathematical models
Derivatives
Derivative

Keywords

  • Age-structured equations
  • Immunity
  • Lyapunov functionals
  • Persistence

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

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abstract = "In this paper, we present an age-structured mathematical model for infectious disease in vivo with infection age of cells. The model contains an immune variable and the effect of absorption of pathogens into uninfected cells. We construct Lyapunov functionals for the model and prove that the time derivative of the functionals are nonpositive. Using this, we prove the global stability results for the model. Especially, we present the full mathematical detail of the proof of the global stability.",
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AB - In this paper, we present an age-structured mathematical model for infectious disease in vivo with infection age of cells. The model contains an immune variable and the effect of absorption of pathogens into uninfected cells. We construct Lyapunov functionals for the model and prove that the time derivative of the functionals are nonpositive. Using this, we prove the global stability results for the model. Especially, we present the full mathematical detail of the proof of the global stability.

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KW - Lyapunov functionals

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