# Effective distances for epidemics spreading on complex networks

@article{Iannelli2017EffectiveDF, title={Effective distances for epidemics spreading on complex networks}, author={Flavio Iannelli and Andreas Koher and Dirk Brockmann and Philipp H{\"o}vel and Igor M. Sokolov}, journal={Physical Review. E}, year={2017}, volume={95} }

We show that the recently introduced logarithmic metrics used to predict disease arrival times on complex networks are approximations of more general network-based measures derived from random walks theory. Using the daily air-traffic transportation data we perform numerical experiments to compare the infection arrival time with this alternative metric that is obtained by accounting for multiple walks instead of only the most probable path. The comparison with direct simulations reveals a…

## 71 Citations

Contact-Based Model for Epidemic Spreading on Temporal Networks

- Computer SciencePhysical Review. X
- 2019

A contact-based model to study the spreading of epidemics by means of extending the dynamic message-passing approach to temporal networks and derives an analytical expression for the epidemic threshold on temporal networks to demonstrate the feasibility of this method on empirical data.

Epidemic extinction in networks: insights from the 12 110 smallest graphs

- MathematicsNew Journal of Physics
- 2018

The expected time to extinction in the susceptible-infectious-susceptible (SIS) model of disease spreading is investigated rather than using stochastic simulations, or asymptotic calculations in network models, and the extinction time is solved exactly for all connected graphs with three to eight vertices.

Estimating epidemic arrival times using linear spreading theory.

- Computer ScienceChaos
- 2018

The dynamics of a spatially structured model of worldwide epidemics is studied and predictions for arrival times of the disease at any city in the network based upon expansion of the heat kernel for the linearized system are presented.

Epidemic spreading on complex networks as front propagation into an unstable state

- Mathematics
- 2021

It is shown that several features of invasion fronts in the PDE context are also relevant to the network case and the susceptible-infected-recovered model on a network is linearly determined in the sense that the departure times in the nonlinear system are approximated by the arrival times of the instability in the system linearized near the disease free state.

Cover time for random walks on arbitrary complex networks

- Computer Science, MathematicsPhysical review. E
- 2017

The results reveal an intimate link between first-passage and cover time statistics and offer a computationally efficient way for estimating cover times in network-related applications.

Reaction-diffusion on random spatial networks with scale-free jumping rates via effective medium theory

- MathematicsPhysical Review. E
- 2018

We study epidemic processes using a metapopulation approach on the line featuring random transport rates between arbitrarily distant sites. An average transport network is found using a recently…

Simulating SIR processes on networks using weighted shortest paths

- Computer ScienceScientific Reports
- 2018

The framework maps the SIR dynamics to weights assigned to the edges of the network, which can be done for Markovian and non-Markovian processes alike, to perform efficient source detection and to improve strategies for time-critical vaccination.

Network centrality based on reaction-diffusion dynamics reveals influential spreaders

- MathematicsArXiv
- 2018

This work connects the two problems of influential spreaders identification and spreading processes' hitting time estimation by introducing a centrality metric, called ViralRank, which quantifies how close a node is, on average, to the other nodes in terms of the random-walk effective distance.

Quantifying transient spreading dynamics on networks.

- PhysicsChaos
- 2018

Generic spreading dynamics in deterministic network dynamical systems close to a given operating point is analyzed and formal expectation values for deterministic dynamics are introduced to work out a theory explicitly quantifying when and how strongly a perturbation initiated at one unit of a network impacts any other.

Calculation of epidemic arrival time distributions using branching processes.

- Computer SciencePhysical review. E
- 2020

By considering the early stages of epidemic spread as a simple branching process, the full probability distribution of arrival times is derived and the robustness of the approach is demonstrated, both to parameter values far outside the traditionally considered regime and to errors in the parameter values used.

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