Analysis for hidden-geometry phenomenon of epidemic spreading in metapopulation networks

Abstract

This paper studies the hidden-geometry phenomenon of epidemic spreading in metapopulation networks. The present study analyses the rationality of mathematical models of the hidden-geometry phenomenon, and shows that invasion threshold can decrease the randomness of disease arrival time such that making the hidden-geometry phenomenon apparent. This study also provides further analytical results of the hidden-geometry phenomenon. First, the max-location invariance property of link-level disease arrival time is revealed. Second, it is shown that the effective speed in the hidden-geometry relationship shall approximately equal to the rate of exponential growth of disease, which could keep almost constant if the proportion of travellers leaving from and reaching at every subpopulation is small. Third, on the basis of analysis for hidden-geometry phenomenon, we show that the mobility rate of infected individuals shall be far larger than the average level.