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

Sun Xiaodan and Huo Xi and Xiao Yanni and Wu Jianhong: Large amplitude and multiple stable periodic oscillations in treatment-donation-stockpile dynamics. (2016)

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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.

Item Type: Journal
Other title: Honoring the career of Tibor Krisztin on the occasion of his sixtieth birthday
Publication full: Electronic journal of qualitative theory of differential equations : special edition
Date: 2016
Volume: 2
Number: 82
ISSN: 1417-3875
Number of Pages: 25
Language: English
DOI: 10.14232/ejqtde.2016.1.82
Uncontrolled Keywords: Differenciálegyenlet
Additional Information: Bibliogr.: p. 22-25. ; összefoglalás angol nyelven
Date Deposited: 2021. Nov. 11. 15:04
Last Modified: 2021. Nov. 12. 09:42

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