The front of the epidemic spread and first passage percolation

In this paper we establish a connection between epidemic models on random networks with general infection times considered in [2] and first passage percolation. Using techniques developed in [6], when each vertex has infinite contagious periods, we extend results on the epidemic curve in [2] from bounded degree graphs to general sparse random graphs with degrees having finite third moments as n ¿ 8. We also study the epidemic trail between the source and typical vertices in the graph. This connection to first passage percolation can be also be used to study epidemic models with general contagious periods as in [2] without bounded degree assumptions