Abstract
A predator-prey model with transmissible disease in the prey species is proposed and analysed. The essential mathematical features are analysed with the help of equilibrium, local and global stability analyses and bifurcation theory. We find four possible equilibria. One is where the populations are extinct. Another is where the disease and predator populations are extinct and we find conditions for global stability of this. A third is where both types of prey exist but no predators. The fourth has all three types of individuals present and we find conditions for limit cycles to arise by Hopf bifurcation. Experimental data simulation and brief discussion conclude the paper.
| Original language | English |
|---|---|
| Pages (from-to) | 911-929 |
| Number of pages | 19 |
| Journal | Mathematical Methods in the Applied Sciences |
| Volume | 30 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - 25 May 2007 |
| Externally published | Yes |
UN SDGs
This output contributes to the following UN Sustainable Development Goals (SDGs)
-
SDG 15 Life on Land
Free Keywords
- Boundedness
- Eco-epidemiology
- Global stability
- Hopf bifurcation
- Local stability
- Predator-prey model
- Simulation
ASJC Scopus subject areas
- General Mathematics
- General Engineering
Fingerprint
Dive into the research topics of 'A predator-prey model with disease in the prey species only'. Together they form a unique fingerprint.Cite this
- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver