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1 results

  • The front of the epidemic spread and first passage percolation

  • Part of
  • Shankar Bhamidi, Remco van der Hofstad, Júlia Komjáthy
  • Journal:
    Journal of Applied Probability / Volume 51 / Issue A / December 2014
    Published online by Cambridge University Press:
    30 March 2016, pp. 101-121
    Print publication:
    December 2014
    • Article
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  • 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 n → ∞, with an appropriate X2log+X condition. We also study the epidemic trail between the source and typical vertices in the graph.