| The dynamics of plant disease epidemics in time is one of the important fields in plant disease epidemiology. Several mathematical functions have been introduced and applied to simulate the seasonal development dynamics and these include monomolecular, exponential, logistic, Gompertz, Weibull and Richards functions. Among these theoretical functions, the Richards function was thought of as a general purpose function in plant disease simulation. However, this function had not been used widely by researchers because it is too complicate, time-consuming in finding out a proper value for the m (progress curve shape) parameter when simulating, and this function has not been incorporated into any existing computer software. So the primary objective of present study was to construct a computer software of using Richards and other theoretical functions.The waterfall model was employed to develop the software system for simulating plant disease epidemic dynamics in time. The best m value of Richards function was determined using the 'golden selection strategy' (or '0.618 strategy') and then the other parameters were computed by regression analysis. For disease epidemic simulations with exponential, monomolecular, logistic and Gompertz functions, the related parameters were estimated directly through regression analysis. The software program was constructed using the Visual Basic language version 6.0 (VB6.0) and packaged with the Wise Installation System (WIS). The program was tested and modified repeatedly for completion and effectiveness. The completed software is able to compute and output simulated disease epidemic models together with its kai-square(χ2), determination coefficient(R), root mean squared error (RMSE) and the curve shape parameter (m). It can also produce simulated progress curves of disease epidemics. In addition, the software can be used to forecast disease intensities and the time at which disease epidemic reaches certain intensity level.The developed software is named Epitimulator (a word formed from the words epidemic, time and simulator). It can be installed and run on personal microcomputers with Windows 98,2000 and XP systems. Data input is easy and convenient: they can be directly keyed in, or be imported from Excel files. The software is extremely fast and only less than 0.1 second of time is consumed to compute and output a simulated model. The displays (windows) are nice and straightforward, rendering the software user-friendly. The output models and related data of parameter can be pasted into Microsoft Excel worksheet and Word for editting as required, and the output simulated disease progress curves can be stored in separate file in bmp format.After the final modification and testing, Epitimulator was applied to simulate the growth curves of two plant fungi and the disease progress curves of three plant diseases.1. Simulation of growth dynamics of fungal plant pathogens: The simulation with Gompertz,logistic and Richards functions embedded in Epitimulator were selected to model the conidiospore germination and colony growth dynamic curves of Fusarium philoxeroides causing Fusarium wilt of alligatorweed and Colletotrichum theae-sinesis causing leaf blight of tea. The results showed that all the three mathematical functions mimicked the growth curves nicely, but the Richards function was the best function to fit the fungal growth dynamics. The simulated models with Richards function were:x=[1-1.8985exp(-0.3193t)]0.8808(m=-0.1354,R=0.9544, x2=0.0344)①x=[1- 39.6891exp(-1.5695t)]3.6881(m=0.7289,R=0.9688, x2=0.0334)②x =[1+2.3145exp(-0.4011t)]-4.0635(m=1.2461,R=0.9896, x2=0.0113)③x=[1+2.2990exp(-0.4445t)]-4.0635(m=1.2461,R=0.9907, x2=0.0131)④(Note: models①,②,③and④are for pore germination dynamics of E philoxeroids and C.theae-inesis, and for colonly growth of two fungi.)2. Simulation of epidemic dynamics of fungal plant diseases: Progress data of rice sheath blight were obtained from field plot experiment. Epitimulator was applied to mimic the progress curves of the 6 disease treatments with initial inoculation intensity of 30,50, 70, 90,110, and 130 grams of R. solani-rice hull inoculum. Simulated models were produced from Gompertz,logistic and Richards functions together values of the model testing parameters and the curve shape parameter (m). These simulations showed that the Richards function is the best mathematical function for mimicking rice sheath blight epidemics. The Richards-simulated models are:x =[1-1.0706exp(-0.0105t)]1.8403(m=0.4566,R=0.9927, x2=0.0016)x =[1+0.1874exp(-0.2139t)]20.5699(m=1.0486,R=0.9822, x2=0.0109)x =[1-0.6957exp(-0.0174t)]3.6881(m=0.7289,R=0.9875, x2=0.0100)x =[1-0.6903exp(-0.2103t)]3.6881(m=0.7300,R=0.9885, x2=0.0109)x =[1- 0.2492exp(-0.0282t)]13.6142(m=0.9265,R=0.9862, x2=0.0166)x =[1+0.6364exp(-0.0432t)]-8.0703(m=1.1239,R=0.9812, x2=0.0227)3. Analysis of the dynamics of corn Northern leaf blight and wheat powdery mildew epidemics: Seasonal development data of the two diseases on different crop cultivars were obtained from literatures and were fitted with different theoretical functions by using the Epitimulator software. Results from the simulation analysis showed that the Gompertz function fitted these epidemics more significantly than the logistic function did, but the Richards was the best function to describe these disease epidemics. The Richards-simulated models of northern leaf blight epidemic on Shendan 14 and Shennong 1 are shown as the follow:x =[1+75.1064exp(-0.1107t)]-0.7135(m=2.4015, R=0.9833, x2=0.0246);x =[1+0.2123exp(-0.0466t)]-20.6238(m=1.0485, R=0.9881, x2=0.0171);The Richards-simulated models of wheat powdery mildew on Yumai 41, Wen 2540, Yumai 13, Yumai 18 are shown as the follow:x =[1+1.5412×l018exp(-0.7559t)]-0.115(m=9.6808,R=0.9851, x2=0.0037);x =[1+6.2364exp(-0.0672t)]-1.7698( m=1.5650, R=0.9317, x2=0683);x=[1+9.4269exp(-0.0785t)]-1.5610(m=1.6406,R=0.9977, x2=0.0026);x =[1+6.2364exp(-0.0672t)]-1.7698(m=1.5650,R=0.9317, x2=0.0683)4. Forecasting sheath blight of rice and Northern leaf blight of corn: Simulated models were obtained from fitting earlier data of rice sheath blight and corn Northern leaf blight with Richards function by using the Epitimulator. These models were applied, respectively, to forecast the later epidemics of the two diseases by using the forecast function of this software. The results indicated that both the disease epidemics were nicely predicated by the simulated empirical models. The forecasting correctness for the two diseases reached 93.4% and 93.5% on average, respectively.
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