A SIMULATION-MODEL TO DESCRIBE EPIDEMICS OF RUST OF PHASEOLUS BEANS .1. DEVELOPMENT OF THE MODEL AND SENSITIVITY ANALYSIS

A simulation model was developed for bean rust epidemics based on infections that occurred in daily cohorts of leaf growth. The most sensitive function in the model was the daily correction of the basic infection rate for the amount of healthy host tissue on each cohort that was available for infection. Components of the basic infection equation, i.e., maximum basic infection rate (R(max)) and parameters for environmental favorability (F) and the rate of the decreased susceptibility of leaves with age (A), also were sensitive factors. A greater pustular area on day 70 occurred when the rate of host growth was slower than standard, and a lower pustular area occurred when the rate of host growth was faster than standard. The maximum leaf area per plant was a relatively in sensitive parameter. The total pustular area (y(70)) was greatest when an epidemic was initiated at the highest level (f(0) = 0.01) of initial infection, on the earliest day of infection [i(f(0)) = 2], and at maximum environmental favorability (F = 1.0). With epidemic rates (k(G)) calculated with the Gompertz transformation, the fastest rates also occurred at f(0) = 0.01, i(f(0)) = 2, and F = 1.0. In contrast, with epidemic rates (r) calculated with the logistic transformation, the fastest rates occurred with epidemics begun at the lowest level (f(0) = 0.00001) of initial infection. The logistic transformation of the low levels of y(50-70) caused inflated values of r. The model was verified by simulating an epidemic using temperatures and hours of leaf wetness that were recorded during an actual season. The curve for the increase in pustular area simulated by the model was representative of the progress of rust observed in the natural epidemic.