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Seminários do IMPA

Probabilidade e Combinatória

Epidemic spreading by random walks on edge-transitive graphs
Giulio Iacobelli

Quarta-feira, 7 de novembro de 2018, 15:30
Sala 333

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