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- Title
Global dynamics of a delayed eco-epidemiological model with Holling type-III functional response.
- Authors
Xu, Rui; Tian, Xiaohong
- Abstract
In this paper, an eco-epidemiological model with Holling type-III functional response and a time delay representing the gestation period of the predators is investigated. In the model, it is assumed that the predator population suffers a transmissible disease. The disease basic reproduction number is obtained. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the disease-free equilibrium and the endemic-coexistence equilibrium are established, respectively. By using the persistence theory on infinite dimensional systems, it is proved that if the disease basic reproduction number is greater than unity, the system is permanent. By means of Lyapunov functionals and LaSalle's invariance principle, sufficient conditions are obtained for the global stability of the endemic-coexistence equilibrium, the disease-free equilibrium and the predator-extinction equilibrium of the system, respectively. Copyright © 2013 John Wiley & Sons, Ltd.
- Subjects
EPIDEMIOLOGICAL models; HOPF bifurcations; STABILITY theory; BASIC reproduction number; LYAPUNOV functions
- Publication
Mathematical Methods in the Applied Sciences, 2014, Vol 37, Issue 14, p2120
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.2960