Modelling and analysis of an eco-epidemiological model with time delay and stage structure

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• 作者：Lingshu Wang ; Rui Xu ; Guanghui Feng
• 关键词：Eco ; epidemiological model ; Stage structure ; Time delay ; LaSalle invariant principle ; Hopf bifurcation ; Stability ; 34K18 ; 34K20 ; 34K60 ; 92D25
• 刊名：Journal of Applied Mathematics and Computing
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：50
• 期：1-2
• 页码：175-197
• 全文大小：713 KB
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• 作者单位：Lingshu Wang (1)
  Rui Xu (2)
  Guanghui Feng (2)
  
  1. School of Mathematics and Statistics, Hebei University of Economics & Business, Shijiazhuang, 050061, People’s Republic of China
  2. Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang, 050003, People’s Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Computational Mathematics and Numerical Analysis
  Applied Mathematics and Computational Methods of Engineering
  Theory of Computation
  Mathematics of Computing
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1865-2085

文摘

A stage-structured predator–prey model with a transmissible disease spreading in the predator population and a time delay due to the gestation of the predator is formulated and analyzed. By analyzing corresponding characteristic equations, the local stability of each feasible equilibria and the existence of Hopf bifurcations at the disease-free equilibrium and the coexistence equilibrium are addressed, respectively. By using Lyapunov functions and the LaSalle invariant principle, sufficient conditions are derived for the global stability of the trivial equilibrium, the predator–extinction equilibrium and the disease-free equilibrium, respectively. Further, sufficient conditions are derived for the global attractiveness of the coexistence equilibrium of the proposed system. Numerical simulations are carried out to support the theoretical analysis. Keywords Eco-epidemiological model Stage structure Time delay LaSalle invariant principle Hopf bifurcation Stability