Epidemic dynamics and patterns of plant diseases

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.