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Stability of the Spread Parameter of the Power Law Model for Dispersal Gradients of Disease Epidemics

Peter Ojiambo: North Carolina State University

<div>Theory and experimental evidence indicate that pathogens that are aerially transmitted over long distances typically have a marginal contact distribution that has a power law tail. Epidemics caused by these pathogens are characterized by a dispersive wave with accelerating velocity of focus expansion. In several plant and animal disease systems, the spread parameter (<em>b</em>) of the power law model has been shown to be approximately 2. This approximation facilitates prediction of the distance travelled by epidemic fronts of dispersive waves. Several factors influence disease spread and expansion of the resultant epidemic, although the stability of <em>b</em> over multiple realizations of an epidemic has not been established. Using cucurbit downy mildew in the eastern United States as a case study, epidemic data collected from 2008 to 2014 were analyzed using a spatio-temporal model of disease spread that incorporates logistic growth in time with a power law function for dispersal. Gradients from temporal and spatial regression models varied by a factor of 2.5 across years, with the corresponding estimates of <em>b</em> ranging from 1.51 to 4.16. Covariance analysis showed a significant interaction between <em>b</em> and time even where data were well described by the power law model. These results indicate that <em>b</em> may not be stable over multiple epidemic years and a value of 2 may be considered the lower limit of the parameter for organisms capable of long-distance dispersal when epidemics are not severely constrained by factors such as host availability.</div>

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