| Issue |
Math. Model. Nat. Phenom.
Volume 9, Number 2, 2014
Epidemics models on networks
|
|
|---|---|---|
| Page(s) | 89 - 107 | |
| DOI | https://doi.org/10.1051/mmnp/20149206 | |
| Published online | 24 April 2014 | |
The Effect of Graph Structure on Epidemic Spread in a Class of Modified Cycle Graphs
Institute of Mathematics, Eötvös Loránd University, Budapest, Hungary and
Numerical Analysis and Large Networks Research Group, Hungarian Academy of Sciences
⋆
Corresponding author. E-mail: simonp@cs.elte.hu
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.
Mathematics Subject Classification: 05C82 / 37N25 / 60J28 / 90B15
Key words: SIS epidemic / theoretical approximation / network process
© EDP Sciences, 2014
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