A simple stochastic model with environmental transmission explains multi-year periodicity in outbreaks of avian flu.

• Main Authors: Rong-Hua Wang, Zhen Jin, Quan-Xing Liu, Johan van de Koppel, David Alonso
• Format: Article
• Language: English
• Published: Public Library of Science (PLoS) 2012-01-01
• Series: PLoS ONE
• Online Access: https://www.ncbi.nlm.nih.gov/pmc/articles/pmid/22363397/pdf/?tool=EBI

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.