According to theory, a focus of disease in a crop expands radially at a rate that asymptotically approaches a constant value. This value can be calculated from the time kernel, contact distribution, and gross reproduction. Time kernel describes the inoculum production through time and contact distribution describes inoculum dispersal. Gross reproduction is the total number of victimized individuals produced by a single infectant placed in a population consisting of suscepts only. Definitions and mathematical evidence are given.
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Bosch et al. (2007) studied this question.