A Simple Stochastic Model with Environmental Transmission Explains Multi-Year Periodicity in Outbreaks of Avian Flu

• Published in: PLoS ONE
• Main Authors: Wang, Rong-Hua, Jin, Zhen, Liu, Quan-Xing, van de Koppel, Johan, Alonso, David
• Format: Text
• Language: English
• Published: Public Library of Science 2012
• Subjects: Research Article; Avian flu
• Online Access: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3281819; http://www.ncbi.nlm.nih.gov/pubmed/22363397; https://doi.org/10.1371/journal.pone.0028873

Avian influenza virus reveals persistent and recurrent outbreaks in North American wild waterfowl, and exhibits major outbreaks at 2–8 years intervals in duck populations. The standard susceptible-infected- recovered (SIR) framework, which includes seasonal migration and reproduction, but lacks environmental transmission, is unable to reproduce the multi-periodic patterns of avian influenza epidemics. In this paper, we argue that a fully stochastic theory based on environmental transmission provides a simple, plausible explanation for the phenomenon of multi-year periodic outbreaks of avian flu. Our theory predicts complex fluctuations with a dominant period of 2 to 8 years which essentially depends on the intensity of environmental transmission. A wavelet analysis of the observed data supports this prediction. Furthermore, using master equations and van Kampen system-size expansion techniques, we provide an analytical expression for the spectrum of stochastic fluctuations, revealing how the outbreak period varies with the environmental transmission.