{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:41:54Z","timestamp":1760784114607,"version":"3.38.0"},"reference-count":23,"publisher":"Cambridge University Press (CUP)","issue":"A","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2014,12]]},"abstract":"<jats:p>We establish a connection between epidemic models on random networks with general infection times considered in Barbour and Reinert (2013) and first passage percolation. Using techniques developed in Bhamidi, van der Hofstad and Hooghiemstra (2012), when each vertex has infinite contagious periods, we extend results on the epidemic curve in Barbour and Reinert (2013) from bounded degree graphs to general sparse random graphs with degrees having finite second moments as<jats:italic>n<\/jats:italic>\u2192 \u221e, with an appropriate<jats:italic>X<\/jats:italic><jats:sup>2<\/jats:sup>log<jats:sup>+<\/jats:sup><jats:italic>X<\/jats:italic>condition. We also study the epidemic trail between the source and typical vertices in the graph.<\/jats:p>","DOI":"10.1017\/s0021900200021227","type":"journal-article","created":{"date-parts":[[2016,3,30]],"date-time":"2016-03-30T16:25:31Z","timestamp":1459355131000},"page":"101-121","source":"Crossref","is-referenced-by-count":6,"title":["The front of the epidemic spread and first passage percolation"],"prefix":"10.1017","volume":"51","author":[{"given":"Shankar","family":"Bhamidi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Remco","family":"van der Hofstad","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J\u00falia","family":"Komj\u00e1thy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,3,30]]},"reference":[{"key":"S0021900200021227_ref18","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20231"},{"volume-title":"Random Measures","year":"1976","key":"S0021900200021227_ref20"},{"key":"S0021900200021227_ref16","doi-asserted-by":"publisher","DOI":"10.2307\/1427068"},{"volume-title":"Branching Processes with Biological Applications","year":"1975","key":"S0021900200021227_ref15"},{"key":"S0021900200021227_ref9","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20401"},{"volume-title":"Random Graph Dynamics","year":"2007","key":"S0021900200021227_ref14"},{"volume":"369","volume-title":"London Math. 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