Abstract
We introduce a path-integral formulation of network-based measures that generalize the concept of geodesic distance and that provides fundamental insights into the dynamics of disease transmission as well as an efficient numerical estimation of the infection arrival time.
Highlights
The forecast and control of emergent diseases has become important in recent years because of the increasingly growing structure and velocity of transportation means
We introduce a path-integral formulation of network-based measures that generalize the concept of geodesic distance and that provides fundamental insights into the dynamics of disease transmission as well as an efficient numerical estimation of the infection arrival time
We have introduced a path-integral formulation of network effective distances by relaxing the assumption of simple-path propagation of spreading processes
Summary
The forecast and control of emergent diseases has become important in recent years because of the increasingly growing structure and velocity of transportation means. Effective distances (ED) in the dominant-path approach can be defined, for both directed and undirected networks, as the geodesic graph distance of a weighted graph with edge weights given by the first moment of a distribution known from extreme events statistics [8], which depends only on the network topology and on the transmission and recovery rates. This approach has the disadvantage that it can significantly overestimate the infection arrival time obtained numerically [5,6].
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