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Global dynamics of a delayed eco‐epidemiological model with Holling type‐III functional response
Author(s) -
Xu Rui,
Tian Xiaohong
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2960
Subject(s) - mathematics , functional response , basic reproduction number , stability (learning theory) , epidemic model , lyapunov function , invariance principle , population , extinction (optical mineralogy) , mathematical economics , type (biology) , stability theory , predation , predator , nonlinear system , ecology , biology , demography , computer science , linguistics , philosophy , physics , paleontology , quantum mechanics , machine learning , sociology
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.