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Relating the Progeny Production Curve to the Speed of an Epidemic

March 2013 , Volume 103 , Number  3
Pages  204 - 215

Francis J. Ferrandino

Associate Scientist, Department of Plant Pathology and Ecology, The Connecticut Agricultural Experiment Station, P.O. Box 1106, New Haven 06504.

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Accepted for publication 13 October 2012.

The dependence of the initial infection rate, r, on the basic reproductive number, R0, and the temporal moments of the progeny production curve are examined. A solution to the linearized Kermack-McKendrick equation is presented and used to analyze a variety of theoretical models of pathogen reproduction. The solution yields a relation between r and the basic reproductive number, R0; the mean time between pathogen generations, μ; and the standard deviation about this mean, σ. A transformation using the dimensionless variables rμ and rσ is introduced, which maps the solution onto a one-dimensional curve. An approximation for the value of r in terms of R0 and the first four temporal moments of the reproductive curve is derived. This allows direct comparison of epidemics resulting from theoretical models with those generated using experimentally obtained reproduction curves. For epidemics characterized by a value of rμ < 5, the value of r is well determined (<2%) by this fourth-order expansion regardless of the functional form of the reproduction curve.

Additional keywords: Laplace Transform, sporulation curve.

© 2013 The American Phytopathological Society