Technical Abstract: Disease spread has traditionally been described as a traveling wave of constant velocity. However, aerially dispersed pathogens capable of long distance dispersal (LDD) often have dispersal gradients with extended tails that could result in acceleration of the epidemic front over time and space. We applied empirical data to a simple model of disease spread that incorporates a logistic equation to describe temporal disease increase and an inverse power function for pathogen dispersal. The model suggests that the position of the epidemic front will increase exponentially with time and that epidemic velocity increases linearly with distance. The scale invariance of the power law dispersal function allowed us to apply the model to spatial scales over five orders of magnitude, from experimental field plots to continental-scale epidemics incorporating both plant and animal diseases. It also may be possible to scale epidemics to account for effects of initial focus size and degree of host heterogeneity. The slope of the inverse power law approximated 2 for the data sets investigated, which would suggest that the position of the epidemic front doubles per unit time and that the slope of velocity plotted against distance is approximately 1/2.