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The Basic Reproduction Number of Plant Pathogens: Matrix Approaches to Complex Dynamics

First and third authors: Department of Biomathematics and Bioinformatics, Rothamsted Research, Harpenden, AL5 2JQ, UK; second author: Scottish Agricultural College, King's Buildings, West Mains Road, Edinburgh EH9 3JG, UK; and fourth author: Department of Plant Pathology, Ohio State University, Wooster, OH 44691-4096.

The basic reproduction number, R₀, is defined as the total number of infections arising from one newly infected individual introduced into a healthy (disease-free) host population. R₀ is widely used in ecology and animal and human epidemiology, but has received far less attention in the plant pathology literature. Although the calculation of R₀ in simple systems is straightforward, the calculation in complex situations is challenging. A very generic framework exists in the mathematical and biomathematical literature, which is difficult to interpret and apply in specific cases. In this paper we describe a special case of this general framework involving the use of matrix population models. Leading by example, we explain the existing mathematical literature on this subject in such a way that plant pathologists can apply the method for a wide range of pathosystems.

Additional keywords:Beet necrotic yellow vein virus, comparative epidemiology, cultivar mixture, landscape, nursery, propagator tree, Plum pox virus.