### 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 |
---|---|

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

## Cite this

Floyd, W., Kay, L., & Shapiro, M. (2012). A Covering-Graph Approach to Epidemics on SIS and SIS-Like Networks.

*Bulletin of Mathematical Biology*,*74*(1), 175-189. http://dx.doi.org/10.1007/s11538-011-9684-y