Phytopathology. 1999 Jun;89(6):495-505. doi: 10.1094/PHYTO.1999.89.6.495.
ABSTRACT An analytical model of a pandemic, initiated by a single focus and spreading over a continent, is developed using foci as the smallest units of disease and fields as the smallest units of host. A few generalizing assumptions lead to a parameter-sparse model that may answer general questions on pandemics in a qualitative manner. For pandemic spread of disease during one season, a 'within-season velocity of pandemic spread,' C, is expressed as a set of integral equations. Reduction of inoculum during the off-season is expressed by a 'survival ratio' of inoculum, epsilon. The effect of the off-season is a 'push-back' of the pandemic front over a distance Deltah. It will be shown how Deltah is related to C and epsilon. The mean pandemic spread over successive years is calculated as the 'polyetic velocity of pandemic spread,' V, which depends on C and the push-back distance. The concept of 'pandemic effectiveness' is parameterized. Relations between the two velocities of pandemic spread and several model parameters are studied. Somewhat unexpectedly, velocities of pandemic spread depend only in a very limited way on field density represented by the 'cropping ratio' zeta. This implies that our model and methods will also apply to situations with inhomogeneous field distributions. The effect of parameter values on rates of severity increase are analyzed. Finally, generalizations of the model are developed and their applications discussed.
摘要 本文以病灶为疾病的最小单位，以地域为宿主的最小单位，建立了一个由单一病灶引发并在大陆范围内传播的大流行分析模型。通过几个推广性假设，得到了一个参数稀疏的模型，它可以以定性的方式回答关于大流行的一般问题。对于一个季节内疾病的大流行传播，用“大流行传播的本季速度”C 来表示一组积分方程。非季节期的接种物减少用接种物的“存活率”ε来表示。非季节期的影响是大流行前沿在距离 Deltah 上的“后推”。将展示如何将 Deltah 与 C 和ε联系起来。连续几年的大流行平均传播速度被计算为“大流行传播的多育速度”V，它取决于 C 和后推距离。“大流行有效性”的概念被参数化。研究了两种大流行传播速度与几个模型参数之间的关系。有点出人意料的是，大流行传播速度仅在非常有限的程度上取决于由“作物比例”ζ表示的地域密度。这意味着我们的模型和方法也将适用于地域分布不均匀的情况。分析了参数值对严重程度增长率的影响。最后，对模型进行了推广，并讨论了它们的应用。
