Long waiting times may be caused by bank notes which exit the money tracking system for a long time, for instance in banks. However, if this were the case the inter-report time statistics would exhibit a fat tail. Analysing the inter-report time distribution we found an exponential decay which suggests that bank notes are passed from person to person at a constant rate. Furthermore, if we assume that humans exit small areas at a constant rate which is equivalent to exponentially distributed waiting times and that bank notes pass from person to person at a constant rate, the distribution of bank note waiting times would also be exponential in contrast to the observed power law. This reasoning permits no other conclusion than a lack of scale in human waiting time statistics.
Based on our analysis we conclude that the dispersal of bank notes and human transmitted diseases can be accounted for by a continuous time random walk process incorporating scale free jumps as well as long waiting time in between displacements. To our knowledge this is the first empirical evidence for such an ambivalent process in nature. Furthermore, the analysis permits a reliable estimate of the spatial and temporal exponents involved, i.e. ft « a « 0.6. We hope that our results will serve future models for the spread of human infectious disease as the key ingredient of dispersal, which can now be accounted for in a realistic way. We believe that these features, when combined with nonlinear epidemiological reaction kinetics, will lead to the emergence of novel types of spatiotemporal patterns.
Was this article helpful?