a simple stochastic model with environmental transmission explains multi-year periodicity in outbreaks of avian flu一个简单的随机模型与环境解释了多年周期性爆发禽流感的传播.pdfVIP

A Simple Stochastic Model with Environmental Transmission Explains Multi-Year Periodicity in Outbreaks of Avian Flu 1,2 1 2 2 3,4 Rong-Hua Wang , Zhen Jin , Quan-Xing Liu , Johan van de Koppel , David Alonso * 1 Department of Mathematics, North University of China, Taiyuan, Shan’xi, People’s Republic of China, 2 Spatial Ecology Department, the Netherlands Institute of Ecology, Yerseke, The Netherlands, 3 Community and Conservation Ecology Group, University of Groningen, Groningen, The Netherlands, 4 Center for Advanced Studies, Spanish Council for Scientific Research, Blanes, Catalunya, Spain 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. Citation: Wang R-H, J