title: A simple stochastic model with environmental transmission explains multi-year periodicity in outbreaks of avian flu.
abstract: 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.
authors.affiliation: Department of Mathematics, North University of China, Taiyuan, Shan'xi, People's Republic of China.
authors.forename: Rong-Hua
authors.initials: RH
authors.lastname: Wang
authors.forename: Zhen
authors.initials: Z
authors.lastname: Jin
authors.forename: Quan-Xing
authors.initials: QX
authors.lastname: Liu
authors.forename: Johan
authors.initials: J
authors.lastname: van de Koppel
authors.forename: David
authors.initials: D
authors.lastname: Alonso
mesh_terms: D000818:Animals; D004196:Disease Outbreaks / Q000706:statistics & numerical data*; D004198:Disease Susceptibility / Q000453:epidemiology; D004372:Ducks / Q000821:virology; D004777:Environment; D009980:Influenza A virus / Q000502:physiology; D005585:Influenza in Birds / Q000453:epidemiology* / Q000635:transmission*; D008954:Models, Biological; D009656:North America / Q000453:epidemiology; D010507:Periodicity; D015995:Prevalence; D013269:Stochastic Processes; D013997:Time Factors