Phytopathology. 2001 Oct;91(10):1001-10. doi: 10.1094/PHYTO.2001.91.10.1001.
ABSTRACT The general Kermack and McKendrick epidemic model (K&M) is derived with an appropriate terminology for plant diseases. The epidemic dynamics and patterns of special cases of the K&M model, such as the Vanderplank differential-delay equation; the compartmental healthy (H), latent (L), infectious (S), and postinfectious (R) model; and the K&M model with a delay-gamma-distributed sporulation curve were compared. The characteristics of the disease cycle are summarized by the basic reproductive number, R(0), and the normalized sporulation curve, i(tau). We show how R(0) and the normalized sporulation curve can be calculated from data in the literature. There are equivalences in the values of the basic reproductive number, R(0), the epidemic threshold, and the final disease level across the different models.However, they differ in expressions for the initial disease rate, r, and the initial infection, Q, because the values depend on the sporulation curve. Expressions for r and Q were obtained for each model and can be used to approximate the epidemic curve by the logistic equation.
摘要 针对植物病害，我们采用了适当的术语来推导出一般的 Kermack 和 McKendrick 传染病模型 (K&M)。我们比较了 K&M 模型的特殊情况，如 Vanderplank 微分时滞方程、包含健康 (H)、潜伏 (L)、感染 (S) 和感染后 (R) 状态的房室模型、以及带有延迟-伽马分布孢殖曲线的 K&M 模型的传染病动力学和模式。通过基本繁殖数 R(0)和标准化孢殖曲线 i(tau)，我们总结了疾病周期的特征。我们展示了如何从文献中的数据计算基本繁殖数 R(0)和标准化孢殖曲线 i(tau)。不同模型的基本繁殖数 R(0)、传染病阈值和最终疾病水平都具有等效性。然而，它们在初始疾病率 r 和初始感染量 Q 的表达式上存在差异，因为这些值取决于孢殖曲线。我们为每个模型都获得了 r 和 Q 的表达式，这些表达式可以用来通过 logistic 方程来近似传染病曲线。
