Stability Switches in a Host–Pathogen Model as the Length of a Time Delay Increases

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• 作者：Jennifer J. H. Reynolds (1)
  Jonathan A. Sherratt (1)
  Andrew White (1)
  
• 关键词：Time delay ; Density ; dependent prophylaxis ; Stability switches ; Population cycles ; Disease modelling ; 92D25
• 刊名：Journal of Nonlinear Science
• 出版年：2013
• 出版时间：December 2013
• 年：2013
• 卷：23
• 期：6
• 页码：1073-1087
• 全文大小：
• 作者单位：Jennifer J. H. Reynolds (1)
  Jonathan A. Sherratt (1)
  Andrew White (1)
  
  1. Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK
  
• ISSN：1432-1467

文摘

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.