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Ecology and Epidemiology

Focus Expansion in Plant Disease. I: The Constant Rate of Focus Expansion. F. van den Bosch, Institute of Theoretical Biology, State University of Leiden, Groenhovenstraat 5, 2311 BT Leiden, The Netherlands; J. C. Zadoks(2), and J. A. J. Metz(3). (2)Laboratory of Phytopathology, Agricultural University, Binnenhaven 9, 6709 PD Wageningen, The Netherlands; (3)Institute of Theoretical Biology, State University of Leiden, Groenhovenstraat 5, 2311 BT Leiden, The Netherlands. Phytopathology 78:54-58. Accepted for publication 8 September 1986. Copyright 1988 The American Phytopathological Society. DOI: 10.1094/Phyto-78-54.

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.