The abundance threshold for plague as a critical percolation phenomenon
The abundance threshold for plague as a critical percolation phenomenon
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DOI：
10.1038/nature07053
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发表时间：
2008-07-31
期刊：
影响因子：
64.8
通讯作者：
Heesterbeek, J. A. P.
中科院分区：
文献类型：
--
作者：
Davis, S.;Trapman, P.;Heesterbeek, J. A. P.
逾渗理论通常与液体通过多孔介质的缓慢流动有关，并应用于物理科学（1）。流行病学应用预计将用于宿主是植物或一定体积的土壤（2，3）的疾病系统，因此在空间中是固定的。然而，没有自然的例子被报道。渗流理论（4）的中心问题是无限连通簇的可能性，在传染病中，它对应于流行病的正概率。哈萨克斯坦大沙鼠（Rhombomys opimus）种群中鼠疫（鼠疫耶尔森氏菌感染）的档案记录表明，只有当宿主建造的洞穴系统中超过0.33个被家庭群体占据时，才会发生动物流行病（5）。这种丰度阈值的潜在机制尚不清楚。在这里，我们提出的证据表明，这是一个渗透阈值，这是由家庭群体之间的运动，运输传染性跳蚤和沙鼠殖民的巨大规模的连续景观之间的规模差异。传统理论预测，当宿主之间的传播依赖于密度时，传染病传播的丰度阈值就会出现，使得基本繁殖数（R（0））随着丰度增加而增加，在阈值处达到1。然而，逾渗阈值是单独的、空间上明确的阈值，其指示系统中的长程连通性并且不与R（0）= 1一致。免疫阈值是试图通过减少易感物种的丰度来控制传染病的理论基础，包括接种疫苗和扑杀野生动物（6-8）。疾病系统中渗透阈值的第一个自然例子引起了对其他入侵阈值的重新评估，例如非洲狮（Panthera leo）中流行性病毒感染的阈值，以及其他疾病系统，例如獾（Meles meles）中的牛结核病（由牛分枝杆菌引起）。
Percolation theory is most commonly associated with the slow flow of liquid through a porous medium, with applications to the physical sciences(1). Epidemiological applications have been anticipated for disease systems where the host is a plant or volume of soil(2,3), and hence is fixed in space. However, no natural examples have been reported. The central question of interest in percolation theory(4), the possibility of an infinite connected cluster, corresponds in infectious disease to a positive probability of an epidemic. Archived records of plague ( infection with Yersinia pestis) in populations of great gerbils ( Rhombomys opimus) in Kazakhstan have been used to show that epizootics only occur when more than about 0.33 of the burrow systems built by the host are occupied by family groups(5). The underlying mechanism for this abundance threshold is unknown. Here we present evidence that it is a percolation threshold, which arises from the difference in scale between the movements that transport infectious fleas between family groups and the vast size of contiguous landscapes colonized by gerbils. Conventional theory predicts that abundance thresholds for the spread of infectious disease arise when transmission between hosts is density dependent such that the basic reproduction number ( R(0)) increases with abundance, attaining 1 at the threshold. Percolation thresholds, however, are separate, spatially explicit thresholds that indicate long- range connectivity in a system and do not coincide with R(0) = 1. Abundance thresholds are the theoretical basis for attempts to manage infectious disease by reducing the abundance of susceptibles, including vaccination and the culling of wildlife(6-8). This first natural example of a percolation threshold in a disease system invites a re- appraisal of other invasion thresholds, such as those for epidemic viral infections in African lions ( Panthera leo), and of other disease systems such as bovine tuberculosis ( caused by Mycobacterium bovis) in badgers ( Meles meles).