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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.

SUBMITTER: Wang RH

PROVIDER: S-EPMC3281819 | biostudies-literature | 2012

REPOSITORIES: biostudies-literature

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

Wang Rong-Hua RH Jin Zhen Z Liu Quan-Xing QX van de Koppel Johan J Alonso David D

PloS one 20120217 2

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 prov ...[more]

PMID: 22363397

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Project description:A large number of highly pathogenic avian influenza (HPAI) H5N1 outbreaks in poultry and wild birds have been reported in Europe since 2005. Distinct spatial patterns in poultry and wild birds suggest that different environmental drivers and potentially different spread mechanisms are operating. However, previous studies found no difference between these two outbreak types when only the effect of physical environmental factors was analysed. The influence of physical and anthropogenic environmental variables and interactions between the two has only been investigated for wild bird outbreaks. We therefore tested the effect of these environmental factors on HPAI H5N1 outbreaks in poultry, and the potential spread mechanism, and discussed how these differ from those observed in wild birds. Logistic regression analyses were used to quantify the relationship between HPAI H5N1 outbreaks in poultry and environmental factors. Poultry outbreaks increased with an increasing human population density combined with close proximity to lakes or wetlands, increased temperatures and reduced precipitation during the cold season. A risk map was generated based on the identified key factors. In wild birds, outbreaks were strongly associated with an increased Normalized Difference Vegetation Index (NDVI) and lower elevation, though they were similarly affected by climatic conditions as poultry outbreaks. This is the first study that analyses the differences in environmental drivers and spread mechanisms between poultry and wild bird outbreaks. Outbreaks in poultry mostly occurred in areas where the location of farms or trade areas overlapped with habitats for wild birds, whereas outbreaks in wild birds were mainly found in areas where food and shelters are available. The different environmental drivers suggest that different spread mechanisms might be involved: HPAI H5N1 spread to poultry via both poultry and wild birds, whereas contact with wild birds alone seems to drive the outbreaks in wild birds.

Project description:BACKGROUND: Individuals continuously exposed to malaria gradually acquire immunity that protects from severe disease and high levels of parasitization. Acquired immunity has been incorporated into numerous models of malaria transmission of varying levels of complexity (e.g. Bull World Health Organ 50:347, 1974; Am J Trop Med Hyg 75:19, 2006; Math Biosci 90:385-396, 1988). Most such models require prescribing inputs of mosquito biting rates or other entomological or epidemiological information. Here, we present a model with a novel structure that uses environmental controls of mosquito population dynamics to simulate the mosquito biting rates, malaria prevalence as well as variability in protective immunity of the population. METHODS: A simple model of acquired immunity to malaria is presented and tested within the framework of the Hydrology, Entomology and Malaria Transmission Simulator (HYDREMATS), a coupled hydrology and agent-based entomology model. The combined model uses environmental data including rainfall, temperature, and topography to simulate malaria prevalence and level of acquired immunity in the human population. The model is used to demonstrate the effect of acquired immunity on malaria prevalence in two Niger villages that are hydrologically and entomologically very different. Simulations are conducted for the year 2006 and compared to malaria prevalence observations collected from the two villages. RESULTS: Blood smear samples from children show no clear difference in malaria prevalence between the two villages despite pronounced differences in observed mosquito abundance. The similarity in prevalence is attributed to the moderating effect of acquired immunity, which depends on prior exposure to the parasite through infectious bites - and thus the hydrologically determined mosquito abundance. Modelling the level of acquired immunity can affect village vulnerability to climatic anomalies. CONCLUSIONS: The model presented has a novel structure constituting a mechanistic link between spatial and temporal environmental variability and village-scale malaria transmission. Incorporating acquired immunity into the model has allowed simulation of prevalence in the two villages, and isolation of the effects of acquired immunity in dampening the difference in prevalence between the two villages. Without these effects, the difference in prevalence between the two villages would have been significantly larger in response to the large differences in mosquito populations and the associated biting rates.

Dataset Information

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

Publications

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

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