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.
Highlights
Understanding the dynamics of infectious diseases in humans has become a increasing focus in public health science [1,2,3]
Susceptible hosts are infected by direct contact with infected individuals with avian influenza viruses (AIV), and by virus particles that persist in the aquatic environment
We have developed a general, fully stochastic hostpathogen model with two routes of transmission: individual-toindividual and environmental transmission
Summary
Understanding the dynamics of infectious diseases in humans has become a increasing focus in public health science [1,2,3]. Disease persistence is determined by chance events when the number of individuals carrying the disease is small, during the early phases of disease invasion, or when total susceptible population size is reduced due to vaccination and/or immunity. In this case, even if invasion is predicted to be successful in deterministic models, i.e., the basic reproductive number (R0) is larger than one, it may totally fail in the corresponding stochastic system, which means that observing a failed invasion in nature does not necessarily imply a population below the deterministic invasion threshold. It is generally accepted that deeper insights are obtained from the mathematical analysis of stochastic systems
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