A Covering-Graph Approach to Epidemics on SIS and SIS-Like Networks

William Floyd, Leslie Kay, Michael Shapiro

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)175-189
Number of pages15
JournalBulletin of Mathematical Biology
Volume74
Issue number1
Early online date12 Oct 2011
Publication statusPublished - Jan 2012

Keywords

  • Social Networks
  • Epidemics
  • Bond percolation
  • covering graph
  • SIR model
  • SIS model

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