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Models for the Spread of Disease: Model Description. K. P. Minogue, Department of Plant Pathology, Cornell University, Ithaca, NY 14853; W. E. Fry, Department of Plant Pathology, Cornell University, Ithaca, NY 14853. Phytopathology 73:1168-1173. Accepted for publication 21 March 1983. Copyright 1983 The American Phytopathological Society. DOI: 10.1094/Phyto-73-1168.

Some relationships between the spatial and temporal characteristics of epidemics are investigated with the aid of two models of plant disease spread. Based on these models, a new measure of the disease gradient (g) is proposed, which provides a simple link between the gradient steepness, the velocity of spread (v), and the apparent infection rate (r): Specifically, the relationship is g = r/v. It is shown that the disease gradient is not an unambiguous measure of host resistance, and a number of relationships are proposed between the components of resistance and the spatial dynamics of the pathogen population. For example, the gradient becomes steeper as the sporulation rate or infectious period increases, but eventually it becomes independent of both variables. The gradient is little affected by the latent period. The velocity of spread is linearly dependent on the standard deviation of the probability function describing spore dispersal.