Towards modeling of epidemic spread: eigenvalue computation

Zifan Liu (1, 2) , Nahid Emad (1, 2) , Soufian Ben Amor (1) , Michel Lamure (3)

1 PRISM - Parallélisme, Réseaux, Systèmes, Modélisation
2 MDLS - Maison de la Simulation
3 UCBL - Université Claude Bernard Lyon 1

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.

Mots clés: Epidemic; pagerank; Complex networks; Non hermitian eigenvalue problem; Sparse matrix

Domaines: Calcul parallèle, distribué et partagé [cs.DC]

Zifan Liu, Nahid Emad, Soufian Ben Amor, Michel Lamure. Towards modeling of epidemic spread: eigenvalue computation. 2014. ⟨hal-01069010⟩