Complex dynamics in a discrete SIS epidemic model with Ricker-type recruitment and disease-induced death

Lei Xiang, Yuyue Zhang, Jicai Huang, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we investigate the complex dynamics in a discrete SIS epidemic model with Ricker-type recruitment and disease-induced death. It is shown that the model has a unique disease-free equilibrium if the basic reproduction number R≤ 1 and a unique endemic equilibrium if R> 1. Sufficient conditions for the locally asymptotic stability of the equilibria are obtained. A detailed bifurcation analysis at the endemic equilibrium reveals that the model undergoes a sequence of bifurcations, including transcritical bifurcation, flip bifurcation and Neimark–Sacker bifurcation, as the parameters vary. Various numerical simulations, including bifurcation diagrams, phase portraits, maximum Lyapunov exponents and feasible sets, are carried out to present complex periodic windows, period-28 points, multiple chaotic bands, fractal basin boundaries, chaotic attractors and the coexistence of period points and three invariant tori, which not only illustrate the theoretical results but also demonstrate more complex dynamical behaviors of the model.

Original languageEnglish (US)
Pages (from-to)4635-4654
Number of pages20
JournalNonlinear Dynamics
Volume104
Issue number4
DOIs
StatePublished - Jun 2021

Keywords

  • Basin of attraction
  • Bifurcation
  • Chaotic attractor
  • Disease-induced mortality
  • Feasible sets
  • Invariant torus
  • Periodic windows
  • Ricker-type recruitment function
  • SIS epidemic model

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Electrical and Electronic Engineering
  • Applied Mathematics

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