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Stability and Hopf bifurcation analysis of an eco-epidemic model with a stage structure
Authors:Xiangyun Shi  Xueyong Zhou
Affiliation:
  • a College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, Henan, PR China
  • b School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, PR China
  • c School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, Jiangsu, PR China
  • Abstract:In this paper, an eco-epidemiological model with a stage structure is considered. The asymptotical stability of the five equilibria, the existence of stability switches about positive equilibrium, is investigated. It is found that Hopf bifurcation occurs when the delay τ passes though a critical value. Some explicit formulae determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, biological explanations and main conclusions are given.
    Keywords:Eco-epidemiology   Stage structure   Delay   Hopf bifurcation
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