In-homogeneous Virus Spread in Networks

Abstract

Our $N$-intertwined model (now called NIMFA) for virus spread in any network with $N$ nodes is extended to a full heterogeneous setting. The metastable steady-state nodal infection probabilities are specified in terms of a generalized Laplacian, that possesses analogous properties as the classical Laplacian in graph theory. The critical threshold that separates global network infection from global network health is characterized via an $N$ dimensional vector that makes the largest eigenvalue of a modified adjacency matrix equal to unity. Finally, the steady-state infection probability of node $i$ is convex in the own curing rate ${\delta }_i$, but concave in the curing rates ${\delta }_j$ of the other nodes $1\le j\ne i\le N$ in the network.

on http://www.nas.ewi.tudelft.nl/people/Piet/TUDelftReports.html

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