Bifurcation Analysis of a Dynamical Model for the Innate Immune Response to Initial Pulmonary Infections

Shujing Shi, Jicai Huang, Jing Wen, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


It has been reported that COVID-19 patients had an increased neutrophil count and a decreased lymphocyte count in the severe phase and neutrophils may contribute to organ damage and mortality. In this paper, we present the bifurcation analysis of a dynamical model for the initial innate system response to pulmonary infection. The model describes the interaction between a pathogen and neutrophilis (also known as polymorphonuclear leukocytes). It is shown that the system undergoes a sequence of bifurcations including subcritical and supercritical Bogdanov-Takens bifurcations, Hopf bifurcation, and degenerate Hopf bifurcation as the parameters vary, and the model exhibits rich dynamics such as the existence of multiple coexistent periodic oscillations, homoclinic orbits, bistability and tristability, etc. Numerical simulations are presented to explain the theoretical results.

Original languageEnglish (US)
Article number2050252
JournalInternational Journal of Bifurcation and Chaos
Issue number16
StatePublished - Dec 30 2020


  • Bogdanov-Takens bifurcation
  • COVID-19
  • Hopf bifurcation
  • Pneumonia
  • coexistence
  • initial infection
  • innate immune
  • multistability

ASJC Scopus subject areas

  • Modeling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics


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