### Abstract

In this paper, an SIS (susceptible-infected-susceptible)-type epidemic propagation is studied on a special class of 3-regular graphs, called modified cycle graphs. The modified cycle graph is constructed from a cycle graph with N nodes by connecting node i to the node i + d in a way that every node has exactly three links. Monte-Carlo simulations show that the propagation process depends on the value of d in a non-monotone way. A new theoretical model is developed to explain this phenomenon. This reveals a new relation between the spreading process and the average path length in the graph.

Original language | English |
---|---|

Pages (from-to) | 89-107 |

Number of pages | 19 |

Journal | Mathematical Modelling of Natural Phenomena |

Volume | 9 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2014 |

### Fingerprint

### Keywords

- Network process
- SIS epidemic
- Theoretical approximation

### ASJC Scopus subject areas

- Modelling and Simulation

### Cite this

*Mathematical Modelling of Natural Phenomena*,

*9*(2), 89-107. https://doi.org/10.1051/mmnp/20149206

**The effect of graph structure on epidemic spread in a class of modified cycle graphs.** / Szabó-Solticzky, A.; Simon, L. P.

Research output: Contribution to journal › Article

*Mathematical Modelling of Natural Phenomena*, vol. 9, no. 2, pp. 89-107. https://doi.org/10.1051/mmnp/20149206

}

TY - JOUR

T1 - The effect of graph structure on epidemic spread in a class of modified cycle graphs

AU - Szabó-Solticzky, A.

AU - Simon, L. P.

PY - 2014

Y1 - 2014

N2 - In this paper, an SIS (susceptible-infected-susceptible)-type epidemic propagation is studied on a special class of 3-regular graphs, called modified cycle graphs. The modified cycle graph is constructed from a cycle graph with N nodes by connecting node i to the node i + d in a way that every node has exactly three links. Monte-Carlo simulations show that the propagation process depends on the value of d in a non-monotone way. A new theoretical model is developed to explain this phenomenon. This reveals a new relation between the spreading process and the average path length in the graph.

AB - In this paper, an SIS (susceptible-infected-susceptible)-type epidemic propagation is studied on a special class of 3-regular graphs, called modified cycle graphs. The modified cycle graph is constructed from a cycle graph with N nodes by connecting node i to the node i + d in a way that every node has exactly three links. Monte-Carlo simulations show that the propagation process depends on the value of d in a non-monotone way. A new theoretical model is developed to explain this phenomenon. This reveals a new relation between the spreading process and the average path length in the graph.

KW - Network process

KW - SIS epidemic

KW - Theoretical approximation

UR - http://www.scopus.com/inward/record.url?scp=84902124984&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84902124984&partnerID=8YFLogxK

U2 - 10.1051/mmnp/20149206

DO - 10.1051/mmnp/20149206

M3 - Article

AN - SCOPUS:84902124984

VL - 9

SP - 89

EP - 107

JO - Mathematical Modelling of Natural Phenomena

JF - Mathematical Modelling of Natural Phenomena

SN - 0973-5348

IS - 2

ER -