### Abstract

One way to describe the spread of an infection on a network is by approximating the network by a random graph. However, the usual way of constructing a random graph does not give any control over the number of triangles in the graph, while these triangles will naturally arise in many networks (e.g. in social networks). In this paper, random graphs with a given degree distribution and a given expected number of triangles are constructed. By using these random graphs we analyze the spread of two types of infection on a network: infections with a fixed infectious period and infections for which an infective individual will infect all of its susceptible neighbors or none. These two types of infection can be used to give upper and lower bounds for R

Original language | English |
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Journal | Theoretical Population Biology |

Volume | 71 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2007 |

### Bibliographical note

Trap07a## Fingerprint Dive into the research topics of 'On analytical approaches to epidemics on networks'. Together they form a unique fingerprint.

## Cite this

Trapman, J. P. (2007). On analytical approaches to epidemics on networks.

*Theoretical Population Biology*,*71*(2). https://doi.org/10.1016/j.tpb.2006.11.002