Department of Botany and Plant Pathology, Oregon State University, 2082 Cordley Hall, Corvallis, OR 97331, USA.
Ecohealth. 2009 Dec;6(4):546-52. doi: 10.1007/s10393-009-0251-z. Epub 2010 Feb 13.
Disease spread has traditionally been described as a traveling wave of constant velocity. However, aerially dispersed pathogens capable of long-distance dispersal often have dispersal gradients with extended tails that could result in acceleration of the epidemic front. We evaluated empirical data with a simple model of disease spread that incorporates logistic growth in time with an inverse power function for dispersal. The scale invariance of the power law dispersal function implies its applicability at any spatial scale; indeed, the model successfully described epidemics ranging over six orders of magnitude, from experimental field plots to continental-scale epidemics of both plant and animal diseases. The distance traveled by epidemic fronts approximately doubled per unit time, velocity increased linearly with distance (slope ~(1/2)), and the exponent of the inverse power law was approximately 2. We found that it also may be possible to scale epidemics to account for initial outbreak focus size and the frequency of susceptible hosts. These relationships improve understanding of the geographic spread of emerging diseases, and facilitate the development of methods for predicting and preventing epidemics of plants, animals, and humans caused by pathogens that are capable of long-distance dispersal.
疾病传播传统上被描述为具有恒定速度的传播波。然而，能够进行长距离扩散的空气传播病原体通常具有扩散梯度，其尾部延长，这可能导致流行病前沿的加速。我们使用一种简单的疾病传播模型来评估经验数据，该模型将时间内的逻辑增长与扩散的逆幂函数结合在一起。幂律扩散函数的标度不变性意味着它适用于任何空间尺度；事实上，该模型成功地描述了从实验性田间小区到植物和动物疾病的大陆范围流行病的六个数量级的流行病。流行病前沿传播的距离大约每单位时间增加一倍，速度与距离呈线性增加（斜率~(1/2)），逆幂律的指数约为 2。我们发现，也可以对流行病进行缩放，以解释初始爆发焦点的大小和易感宿主的频率。这些关系有助于更好地了解新发疾病的地理传播，并促进开发预测和预防由能够进行长距离扩散的病原体引起的植物、动物和人类流行病的方法。
