Dispersive Epidemic Waves: I. Focus Expansion within a Linear Planting

The three-dimensional, turbulent dispersal of airborne spores yielded epidemiological contact distributions characterized by a length scale that continually increased with increasing downwind distance. This behavior was due to the escape of spores from the plant canopy into the faster moving air above. Such contact distributions approached an inverse power law of distance at large distances. Simulated epidemics based on this type of spore dispersal exhibited spatial disease gradients that became more shallow as the epidemic progressed. Isopathic velocities were related linearly to distance from the focus of disease, irrespective of disease severity. Thus, the leading edge of this dispersive epidemic wave propagated more quickly than did the trailing edge; as a result, the wave spread out in space with increasing time. This behavior contrasted the constant isopathic velocities characteristic of the traveling wave description predicted by spatial contact distributions of an exponential order that had a bounded length scale. A traveling wave description is appropriate if the spatial coordinate is log-transformed first.