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Seminários do IMPA

Probabilidade e Combinatória

Título |
Epidemic spreading by random walks on edge-transitive graphs |

Expositor |
Giulio Iacobelli
UFRJ |

Data |
Quarta-feira, 7 de novembro de 2018, 15:30 |

Local |
Sala 333 |

Resumo |

We study an SIS epidemic model with infections carried by mobile agents performing independent random walks on a graph. Agents can be either infected (I) or susceptible (S), and infection occurs when an infected agent meets a susceptible one. After a recovery time, an infected agent returns to state S and can be infected again. The End of Epidemic (EoE) denotes the first time when all agents are in state S, since after this moment no further infection can occur.

We present some preliminary results for the case of two agents on edge-transitive graphs. Specifically, we characterize EoE as a function of the network structure by relating the Laplace transform of EoE to the Laplace transform of the meeting time of two random walks. We also study the asymptotic behavior of EoE (asymptotically in the size of the graph) on complete graphs, complete bipartite graphs, and rings.

This is joint work with Seva Shneer and Daniel Figueiredo