Abstract
In this paper, we introduce a new class of epidemics on networks which we call SI(S/I). SI(S/I) networks differ from SIS networks in allowing an infected individual to become reinfected without first passing to the susceptible state. We use a covering-graph construction to compare SIR, SIS, and SI(S/I) networks. Like the SIR networks that cover them, SI(S/I) networks exhibit infection probabilities that are monotone with respect to both transmission probabilities and the initial set of infectives. The same covering-graph construction allows us to characterize the recurrent states in an SIS or SI(S/I) network with reinfection.
Original language | English |
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Pages (from-to) | 175-189 |
Number of pages | 15 |
Journal | Bulletin of Mathematical Biology |
Volume | 74 |
Issue number | 1 |
Early online date | 12 Oct 2011 |
Publication status | Published - Jan 2012 |
Keywords
- Social Networks
- Epidemics
- Bond percolation
- covering graph
- SIR model
- SIS model