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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061, USA

    William Floyd & Leslie Kay

  2. Department of Pathology, Tufts University, Boston, MA, 02111, USA

    Michael Shapiro

Authors
  1. William Floyd
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  2. Leslie Kay
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  3. Michael Shapiro
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Correspondence to William Floyd.

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Floyd, W., Kay, L. & Shapiro, M. A Covering-Graph Approach to Epidemics on SIS and SIS-Like Networks. Bull Math Biol 74, 175–189 (2012). https://doi.org/10.1007/s11538-011-9684-y

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  • DOI: https://doi.org/10.1007/s11538-011-9684-y

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