Weibull dynamics and power-law diffusion of epidemics in small world 2D networks

Abstract

We demonstrate that the Weibull statistics characterize the time dependence of the epidemic spread in several idealized cases on 2-D Cartesian lattices, with and without small world structure. These cases include infection from nearest and next nearest neighbors; infection from long-distant neighbors; infection due to external influence. The Weibull closed form for the aggregated disease propagation is used as an analytic tool to elucidate the effect of small world topology in the diffusion scaling. It may be also used to formalize and contain the extensive diversity of real life cases. Along these lines, besides the straightforward implementation of the studied cases in epidemiology, our work proposes a power-law scaling in the Bass model for applications in the diffusion of the technological innovation.