A General Model for Disease Progress with Functions for Variable Latency and Lesion Expansion on Growing Host Plants

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Abstract
A disease-progress model was derived by combining an infection model with a host-growth model. Variants of common growth functions (e.g., the logistic, Gompertz, and exponential) were used at the basic equations to calculate infections and host growth in time. The model contained a feedback mechanism to limit host growth as increased disease. Variable latency was achieved by a distributed-delay submodel. The duration and shape of the latency curve could be altered by changing the number of stages in the submodel and by varying the development rates between stages. As in natural pathosystems, the simulated epidemic rates were faster at lower initial amounts of disease. The epidemic rate after an epidemic interruption was about 2-fold faster than the average rate. The increases in epidemic rate could be explained solely by the amount and proportion of healthy tissue rather than by a change in any variable related to the pathogen. The rate and shape of the plant-growth curve affected the rate and shape of the disease-progress curve. Under some conditions, the areas of healthy and disease tissue could be increasing at exponential rates but the epidemic rate was about zero; i.e., the proportion of disease did not change. If the rates of infection and host growth for a pathosystem are set as functions of environmental parameters, then the general model might be used for real-time simulation. The model may have benefit for decision-making in disease management and to estimate potential crop loss.