Geometric stability switch criteria in delay differential equations with two delays and delay dependent parameters

Qi An, Edoardo Beretta, Yang Kuang, Chuncheng Wang, Hao Wang

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Most modeling efforts involve multiple physical or biological processes. All physical or biological processes take time to complete. Therefore, multiple time delays occur naturally and shall be considered in more advanced modeling efforts. Carefully formulated models of such natural processes often involve multiple delays and delay dependent parameters. However, a general and practical theory for the stability analysis of models with more than one discrete delay and delay dependent parameters is nonexistent. The main purpose of this paper is to present a practical geometric method to study the stability switching properties of a general transcendental equation which may result from a stability analysis of a model with two discrete time delays and delay dependent parameters that dependent only on one of the time delay. In addition to simple and illustrative examples, we present a detailed application of our method to the study of a two discrete delay SIR model.

Original languageEnglish (US)
Pages (from-to)7073-7100
Number of pages28
JournalJournal of Differential Equations
Volume266
Issue number11
DOIs
StatePublished - May 15 2019

Keywords

  • Characteristic equation
  • Delay differential equation
  • Epidemic model
  • Stability switch

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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