VIEW ARTICLE

Ecology and Epidemiology

Focus Expansion in Plant Disease. II: Realistic Parameter-Sparse Models. 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 78:59-64. Accepted for publication 8 September 1986. Copyright 1988 The American Phytopathological Society. DOI: 10.1094/Phyto-78-59.

In a previous paper, a model was presented applicable to the expansion of plant disease foci. The model permits calculating the velocity of focus expansion and the slope of the focal front in a few seconds of microcomputer time. In this paper, a parameter-sparse and yet sufficiently flexible subclass of models is considered that can easily be adapted to various pathosystems. A mechanistic submodel is introduced for the dispersal of infectious units, based on turbulent diffusion inside the canopy and random interception of infectious units by host plants. It describes the contact distribution, a concept analogous to the primary gradient of a focus. The production of infectious units as a function of the time after infection is described by a shifted gamma density. These submodels are shown to fit some published data sets. With the resulting model, the effect of various parameters of contact distribution and time kernel submodels on the velocity of the expanding focus and the slope of its front was investigated.