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arXiv · 0909.3811

Epidemic threshold for the SIS model on networks

Roni Parshani·Shai Carmi·Shlomo Havlin
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Abstract

We derive an analytical expression for the critical infection rate r_c of the susceptible-infectious-susceptible (SIS) disease spreading model on random networks. To obtain r_c, we first calculate the probability of reinfection, pi, defined as the probability of a node to reinfect the node that had earlier infected it. We then derive r_c from pi using percolation theory. We show that pi is governed by two effects: (i) The requirement from an infecting node to recover prior to its reinfection, which depends on the disease spreading parameters; and (ii) The competition between nodes that simultaneously try to reinfect the same ancestor, which depends on the network topology.

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Roni Parshani, Shai Carmi, Shlomo Havlin. 2010-07-14. Epidemic threshold for the SIS model on networks. https://doi.org/10.1103/physrevlett.104.258701

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