Large amplitude and multiple stable periodic oscillations in treatment-donation-stockpile dynamics

Xiaodan Sun, Xi Huo, Yanni Xiao, Jianhong Wu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


A transmission-treatment-donation-stockpile model was originally formulated for the 2014-2015 West Africa Ebola outbreak in order to inform policy complication of large scale use and collection of convalescent blood as an empiric treatment. Here we reduce this model to a three dimensional system with a single delay counting for the duration between two consecutive donations. The blood unit reproduction number R0 is calculated and interpreted biologically. Using the LaSalle’s invariance principle we show that the zero blood bank storage equilibrium is globally asymptotically stable if R0 < 1. When R0 > 1, the system has a non-zero equilibrium with potential occurrence of Hopf bifurcations. The geometric approach previously developed is applied to guide the location of critical bifurcation points. Numerical analysis shows that variations of the single delay parameter can trigger bi-stable large amplitude periodic solutions. We therefore suggest that this time lag must be carefully chosen and maintained to attain stable treatment availability during outbreaks.

Original languageEnglish (US)
Article number82
JournalElectronic Journal of Qualitative Theory of Differential Equations
StatePublished - 2016
Externally publishedYes


  • Convalescent blood transfusion
  • Large amplitude periodic solutions
  • Multiple stable periodic solutions

ASJC Scopus subject areas

  • Applied Mathematics


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