Abstract
The role of disease in ecological systems is a very important issue from both mathematical and ecological points of view. This paper deals with the qualitative analysis of a prey-dependent predator-prey system in which a disease is spreading among the prey species only. We have analysed the behaviour of the system around each equilibrium and obtained conditions for global stability of the system around an equilibrium by using suitable Lypunov functions. We have also worked out the region of parametric space under which the system enters a Hopf bifurcation and a transcritical bifurcation but does not experience either saddle-node bifurcations or pitchfork bifurcations around the disease-free equilibrium E2. Finally, we have given an example of a real ecological situation with experimental data simulations.
| Original language | English |
|---|---|
| Pages (from-to) | 163-178 |
| Number of pages | 16 |
| Journal | Mathematical and Computer Modelling of Dynamical Systems |
| Volume | 13 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Apr 2007 |
| Externally published | Yes |
Keywords
- Eco-epidemiology
- Global stability
- Hopf bifurcation
- Local stability
- Pitchfork bifurcation
- Saddle-node bifurcation
- Transcritical bifurcation
ASJC Scopus subject areas
- Control and Systems Engineering
- Software
- Modelling and Simulation
- Computer Science Applications
- Applied Mathematics
