Stability switches in a host-pathogen model as the length of a time delay increases

Jennifer J H Reynolds, Jonathan Adam Sherratt, Andrew White

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The destabilising effects of a time delay in mathematical models are well known. However, delays are not necessarily destabilising. In this paper, we explore an example of a biological system where a time delay can be both stabilising and destabilising. This example is a host-pathogen model, incorporating density-dependent prophylaxis (DDP). DDP describes when individual hosts invest more in immunity when population densities are high, due to the increased risk of infection in crowded conditions. In this system, as the delay length increases, there are a finite number of switches between stable and unstable behaviour. These stability switches are demonstrated and characterised using a combination of numerical methods and analysis.

Original languageEnglish
Pages (from-to)1073-1087
Number of pages15
JournalJournal of Nonlinear Science
Volume23
Issue number6
DOIs
Publication statusPublished - 1 Dec 2013

Keywords

  • Time delay
  • Density-dependent prophylaxis
  • Stability switches
  • Population cycles
  • Disease modelling
  • DENSITY-DEPENDENT PROPHYLAXIS
  • POPULATION-DYNAMICS
  • DISEASE RESISTANCE
  • FOREST INSECTS
  • CYCLES
  • TRANSMISSION
  • INVERTEBRATE
  • LEPIDOPTERA
  • EQUATIONS
  • SYSTEMS

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