<div dir="ltr"><font face="arial, sans-serif"><div style="font-family:Arial,Helvetica,sans-serif;text-align:center"><font face="arial, sans-serif"><div style="text-align:left"><font color="#000000">Caros colegas,</font></div><div style="text-align:left"><font color="#000000"><br></font></div><div style="text-align:left">na próxima <b>sexta-feira</b>, 27 de novembro, às <b>15h, </b>acontecerá o último seminário do ciclo SPSP-IME-USP de 2020. As informações e os vídeos dos seminários estão disponíveis em <a href="https://sites.google.com/usp.br/psps-ime-usp" target="_blank">https://sites.google.com/usp.br/psps-ime-usp</a>.</div></font><font face="arial, sans-serif"><div style="text-align:left"><br></div></font><font face="arial, sans-serif"><div style="text-align:left">Um abraço,</div><div style="text-align:left">Aline Duarte</div></font></div><div style="font-family:Arial,Helvetica,sans-serif;font-size:large">-------------------------------------</div><div style="font-family:Arial,Helvetica,sans-serif;font-size:large;text-align:center"><br></div><div style="font-family:Arial,Helvetica,sans-serif;font-size:large;text-align:center"><span style="font-size:small"><font size="4" color="#0000ff"><b>Seminar on Probability and Stochastic Processes</b></font></span></div><div style="text-align:center"><span style="box-sizing:border-box;color:rgb(33,33,33);font-variant-ligatures:none;white-space:pre-wrap"><span style="font-weight:700;box-sizing:border-box"><br></span></span></div><div style="text-align:center"><span style="color:rgb(33,33,33);font-variant-ligatures:none;text-align:start;white-space:pre-wrap"> </span><span style="font-variant-numeric:normal;font-variant-east-asian:normal;color:rgb(33,33,33);background-color:transparent;vertical-align:baseline;white-space:pre-wrap"> </span><span style="color:rgb(33,33,33);font-variant-ligatures:none;white-space:pre-wrap"> </span><span style="box-sizing:border-box;color:rgb(33,33,33);font-variant-ligatures:none;white-space:pre-wrap;vertical-align:baseline"><span style="font-weight:700;box-sizing:border-box">Giulio Iacobelli</span></span><span style="color:rgb(33,33,33);font-variant-ligatures:none;white-space:pre-wrap"> - (IM-UFRJ</span><span style="color:rgb(33,33,33);font-variant-ligatures:none;white-space:pre-wrap">)</span></div></font><font face="arial, sans-serif"><div style="text-align:center"><span style="background-color:transparent;white-space:pre-wrap;color:rgb(204,0,0)">Next Friday, November 27th - </span><b style="background-color:transparent;white-space:pre-wrap;color:rgb(204,0,0)">3pm</b></div></font><div><div style="text-align:center"><font face="arial, sans-serif"><span style="color:rgb(33,33,33);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;vertical-align:baseline;white-space:pre-wrap">Live on Google Meets: </span><a href="https://meet.google.com/htw-ctsn-uua" target="_blank">https://meet.google.com/htw-ctsn-uua</a></font></div><div style="text-align:center"><font face="arial, sans-serif">Video recording will be available on: <a href="https://sites.google.com/usp.br/psps-ime-usp" target="_blank">https://sites.google.com/usp.br/psps-ime-usp</a></font></div><div><font face="arial, sans-serif"><br></font></div><div style="text-align:center"><font face="arial, sans-serif"><br></font></div><div><font face="arial, sans-serif"><span style="box-sizing:border-box;color:rgb(33,33,33);font-variant-ligatures:none;white-space:pre-wrap"><span style="font-weight:700;box-sizing:border-box">Title</span></span><span style="color:rgb(33,33,33);font-variant-ligatures:none;white-space:pre-wrap">: </span>Epidemic spreading by random walks on edge-transitive graphs</font></div><div class="gmail_default" style=""><div class="gmail_default"><div class="gmail_default"><font face="arial, sans-serif"><br></font></div></div></div><div><span style="color:rgb(33,33,33);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;vertical-align:baseline;white-space:pre-wrap"><span style="background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;vertical-align:baseline"><font face="arial, sans-serif"><p dir="ltr" style="box-sizing:border-box;font-variant-ligatures:none;margin:0px;outline:none;text-decoration-line:inherit;line-height:1.6;padding-top:0px;padding-left:0px"><span style="box-sizing:border-box"><span style="font-weight:700;box-sizing:border-box">Abstract:</span></span> <span style="font-variant-ligatures:normal;color:rgb(34,34,34)">We study an SIS epidemic model with infections carried by mobile agents performing independent random walks on a graph. Agents can either be infected (I) or susceptible (S),  and an 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 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.</span></p></font></span></span><p><font face="arial, sans-serif">This is joint work with Seva Shneer (<span style="font-size:16.7411px">Heriot-Watt University</span>) and Daniel Figueiredo (COPPE/UFRJ).</font></p></div></div></div>