模拟植物病害流行时间动态的通用模型——Richards函数

RICHARDS FUNCTION: A GENERAL MODEL AND ITS APPLICATION IN STUDYING PLANT DISEASE EPIDEMICS IN TIME

本文介绍了Richards生长函数及其在植物病害流行时间动态模拟中的应用。该函数的微分形式为(dx)/(dt)=rx[(1/x)^(1-m)-1]/(1-m),式中r为病害发展的速率,x表t日期的病情值率(0<x<1),m为流行曲线的形状参数。当m=0,m→1,m=2和m→∞时,从理论上证明Richards函数成为单分子、Compertz、Logistic和指数函数模型。以水稻纹枯病和马铃薯晚疫病的田间进展曲线进行摸拟分析发现,当m取值适当时还可获得较Gompertz或Logistic更逼真的Richards病害曲线拟合模型,而适当m取值的Richards模型比小分子模型对玉米粗缩病的拟合性也更好。因此认为,Richards函数是植病流行时间动态的通用模型。

In this paper are discussed the Richards function, its generality in modelling the dynamics of plant epidemics in time, and its practical appli- cation. The differential form of the function writes: (dx)/(dt)=rx(((1/x)^(1-n-1))/(1-m)), where r is the rate of epidemic development, x the diseased portion of host at time t,and m a parameter indicating the shape or type of disease progress curves.Richards function becomes Monomolecular, Gompertz, Logistic and Exponential model respectively when m=0,m→1,m=2 and m→∞. Application of the models in analyses showed that the epidemics of rice sheath blight and potato late blight could be described by both Logistic and Gompertz models, the epidemics of maize rough dwarf virus by Monomolecular, but Richards model fitted all these epidemic curves best with highest determination coefficients and lowest root mean square errors when the most appropriate m value was chosen for each disease. The Richards function may thus be concluded a general purpose model for simulation of plant disease development in time.