Department of Plant Pathology and Ecology, the Connecticut Agricultural Experiment Station, NH, USA.
Phytopathology. 2013 Mar;103(3):204-15. doi: 10.1094/PHYTO-04-12-0093-R.
The dependence of the initial infection rate, r, on the basic reproductive number, R(0), and the temporal moments of the progeny production curve are examined. A solution to the linearized Kermack-McKendrick equation is presented and used to analyze a variety of theoretical models of pathogen reproduction. The solution yields a relation between r and the basic reproductive number, R(0); the mean time between pathogen generations, μ; and the standard deviation about this mean, σ. A transformation using the dimensionless variables rμ and rσ is introduced, which maps the solution onto a one-dimensional curve. An approximation for the value of r in terms of R(0) and the first four temporal moments of the reproductive curve is derived. This allows direct comparison of epidemics resulting from theoretical models with those generated using experimentally obtained reproduction curves. For epidemics characterized by a value of rμ < 5, the value of r is well determined (<2%) by this fourth-order expansion regardless of the functional form of the reproduction curve.
考察了初始感染率 r 与基本繁殖数 R(0)以及后代产生曲线时间点的关系。给出了 Kermack-McKendrick 线性化方程的解，并用于分析病原体繁殖的各种理论模型。该解给出了 r 与基本繁殖数 R(0)、病原体代际平均时间 μ 以及该平均值的标准差 σ 之间的关系。引入了一个使用无量纲变量 rμ 和 rσ 的变换，将解映射到一维曲线上。根据生殖曲线的前四个时间点导出了 r 关于 R(0)的近似值。这允许使用理论模型产生的流行情况与使用实验获得的生殖曲线产生的流行情况进行直接比较。对于 rμ<5 的流行病，无论生殖曲线的函数形式如何，这个四阶展开都能很好地确定 r 的值（<2%）。
