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Stability Analysis of an Eco-epidemiological Model with Time Delay and Holling Type-III Functional Response
  
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KeyWord:Eco-epidemiological model; Time delay; Holling type-III functional response; Stability; Hopf bifurcation
Author NameAffiliation
Lingshu Wang School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang, Hebei 050061, China 
Mei Zhang School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang, Hebei 050061, China 
Xu Chen School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang, Hebei 050061, China 
Guang Yang School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang, Hebei 050061, China 
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Abstract:
      In this paper, an eco-epidemiological model with diseases in the predator and Holling type-III functional response is analyzed. A time delay due to the gestation of the predator is considered in this model. 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 Lyapunov functionals and LaSalle's invariance principle, sufficient conditions are obtained for the global stability of the predator-extinction equilibrium, the disease-free equilibrium and the endemic-coexistence equilibrium respectively. Finally, numerical simulations are performed to illustrate the theoretical results.