Dynamical analysis and simulation of a 2-dimensional disease model with convex incidence

Pei Yu, Wenjing Zhang, Lindi M. Wahl

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In this paper, a previously developed 2-dimensional disease model is studied, which can be used for both epidemiologic modeling and in-host disease modeling. The main attention of this paper is focused on various dynamical behaviors of the system, including Hopf and generalized Hopf bifurcations which yield bistability and tristability, Bogdanov-Takens bifurcation, and homoclinic bifurcation. It is shown that the Bogdanov-Takens bifurcation and homoclinic bifurcation provide a new mechanism for generating disease recurrence, that is, cycles of remission and relapse such as the viral blips observed in HIV infection.

Original languageEnglish
Pages (from-to)163-192
Number of pages30
JournalCommunications in Nonlinear Science and Numerical Simulation
StatePublished - Aug 1 2016



  • Bogdanov-Takens (BT) bifurcation
  • Dynamical system
  • HIV viral blips
  • Homoclinic orbit
  • Hopf and generalized Hopf bifurcations
  • Recurrent autoimmune disease
  • Recurrent infection
  • Stability and bifurcation

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