Abstract

One transcendental aspect of epidemiology is to predict the evolution of infectious diseases, especially in cases of pandemic outbreaks. In the last decade the emphasis has been placed in the spatial progression of epidemics. Percolation models have been proposed that describe the progress of parasitic infestations and epidemics. In this study, we propose a model that connects the temporal and spatial progress of a global epidemic, determining the time at which an epidemic outbreak becomes a pandemic based on the percolation threshold. First, we propose a simple model of the temporal progression of the geographic progress of epidemics. By means of simulation, we estimate the percolation threshold of epidemics at two scales: global and local. Then, we connect both approaches, determining the time at which this threshold is reached (the critical time of percolation). The advanced model yields a logistic progress of infected localities over time. The estimated percolation thresholds were approximately 59% of the infected localities at local and global scales, and these were not different from the theoretical percolation threshold of square grids. We propose an easy method for following and predicting the geographical progression of infectious disease over time at several scales. Another remarkable aspect of the advanced model is that it allows us to define a pandemic in a more precise form, such as the state of and epidemics in which the percolation threshold is reached, changing the current definition of epidemics in phase 6 (the pandemic phase).