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Mathematical Medicine and Biology 1998 15(2):117-134; doi:10.1093/imammb/15.2.117
© 1998 by Institute of Mathematics and its Applications
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A model for dispersal of plant pathogens by rainsplash

A. PIELAAT* and F. van den BOSCH

Wageningen Agricultural University Dreijenlaan 4, 6703 HA Wageningen, The Netherlands

* E-mail Annemarie.Pielaat{at}zrw.wk.wau.nl

A mechanistic random ‘jump’ model is developed to describe the stochastic processes of splash dispersal of plant pathogens from a point source. In this model the main physical processes involved in the spatial spread of these spores are incorporated. That is, the probability per time unit that a spore is splashed {lambda}, the probability that it then travels over some distance D(x), and the probability that it is not removed during this dispersal process {varepsilon}. Numerical analysis shows the importance of ground cover and rain intensity on the model output. Factors influencing the process can be captured by changing the parameter values. For high rain intensities {lambda} is large, therefore more spores are splashed; and, since {varepsilon} is expressed per splash, simultaneously more spores will be removed from the system. The effect of ground cover is captured by {varepsilon} its value decreases if the probability of staying in the process decreases. In addition, an equation is derived for the mean squared distance that spores splash. This equation shows a linear function independent of D(x). Finally, a diffusion approximation is developed for the mechanistic model and is compared to a diffusion model for splash dispersal developed by Yang et al. (1991a), New Phtol. 118, 295–301. The diffusion equation can only be considered a reasonable approximation to the full model under certain limiting conditions.

Keywords: splash dispersal; spores; random walk; stochastic process


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