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

被引：17

作者：

Wang L. ^{[1
]}

Xu R. ^{[2
]}

Feng G. ^{[2
]}

机构：

[1] School of Mathematics and Statistics, Hebei University of Economics & Business, Shijiazhuang

[2] Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang

来源：

Journal of Applied Mathematics and Computing | 2016年 / 50卷 / 1-2期

基金：

中国国家自然科学基金;

关键词：

Eco-epidemiological model; Hopf bifurcation; LaSalle invariant principle; Stability; Stage structure; Time delay;

D O I：

10.1007/s12190-014-0865-3

中图分类号：

学科分类号：

摘要：

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. © 2015, Korean Society for Computational and Applied Mathematics.

引用

页码：175 / 197

页数：22

共 19 条

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