Travel with Waiting Time and Distance Distributions
This Demonstration models human travel in which the user gets to select the distributions from which (1) random resting times are drawn and (2) random distance jumps are drawn. Such models have been shown to realistically model modern human behavior and are useful in, among other matters, predicting the spread of epidemics.
You select the number of travels and the parameters of both the waiting time distribution and jump distance distribution. You also select whether a Gamma distribution or a Lévy distribution is used. The Demonstration shows the probability density function (PDF) of the resulting distribution in a blue frame. You also select whether travelers within a user-selectable proximity of each other are shown as linked by a line. This control permits you to visualize circumstances under which there might be an interchange among travelers, such as the exchange of an idea or a disease. Finally you select the animation rate, which is calibrated to represent a certain number of days per second. The Demonstration models one year of behavior.
This Demonstration is inspired by D. Brockmann, L. Hufnagel, and T. Geisel, "The Scaling Laws of Human Travel," Nature, 439(7075), 2006 pp. 462–465, (also available here), and the further work of these scholars.
The abstract world examined in this Demonstration has periodic boundaries.