Towards modeling of epidemic spread: eigenvalue computation
Résumé
The eigenvalue equation intervenes in models of infectious disease propa- gation and could be used as an ally of vaccination campaigns in the actions carried out by health care organizations. The epidemiological modeling tech- niques can be considered by analogy, as computer viral propagation which depends only on the underlying graph status at a given time. We point out pagerank as method to study the epidemic spread and consider its calculation in the context of small-world phenomenon. Basing on Baraba ́si-Albert power law graphs, we adapt the model to make the matrix involved have a large and sparse structure, so that numerical methods based on matrix-vector prod- ucts could be employed. We propose to use the implicitly restarted Arnoldi method and introduce its adapted parallel algorithm for the case of very large social graphs.
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