Name
Abstract | ||
|---|---|---|
We study the SIR epidemic model with infections carried by k particles making independent random walks on a random regular graph. We give a edge-weighted graph reduction of the dynamics of the process that allows us to apply standard results of Erdös-Renyi random graphs on the particle set. In particular, we show how the parameters of the model produce two phase transitions: In the subcritical regime, O(ln k) particles are infected. In the supercritical regime, for a constant C determined by the parameters of the model, Ck get infected with probability C, and O(ln k) get infected with probability (1-C). Finally, there is a regime in which all k particles are infected. Furthermore, the edge weights give information about when a particle becomes infected. We demonstrate how this can be exploited to determine the completion time of the process by applying a result of Janson on randomly edge weighted graphs. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1214/13-AAP1000 | Annals of Applied Probability |
Keywords | DocType | Volume |
sir epidemic model,constant c,edge weight,random regular graph,ln k,supercritical regime,subcritical regime,independent random walk,viral process,s-renyi random graph,k particle,random graphs,random walks | Conference | 25 |
Issue | ISSN | Citations |
2 | Annals of Applied Probability 2015, Vol. 25, 477-522 | 1 |
PageRank | References | Authors |
0.35 | 14 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mohammed Abdullah | 1 | 4 | 0.81 |
| Colin Cooper | 2 | 857 | 91.88 |
| Moez Draief | 3 | 168 | 18.57 |