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 language | English |
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Pages (from-to) | 1073-1087 |
Number of pages | 15 |
Journal | Journal of Nonlinear Science |
Volume | 23 |
Issue number | 6 |
DOIs | |
Publication status | Published - 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