Limit theorems for an epidemic model on the com-plete graph

Thomas Kurtz, Elcio Lebensztayn, Alexandre Leichsenring, Fábio Machado
2008 Alea   unpublished
We study the following random walks system on the complete graph with n vertices. At time zero, there is a number of active and inactive particles living on the vertices. Active particles move as continuous-time, rate 1, random walks on the graph, and, any time a vertex with an inactive particle on it is visited, this particle turns into active and starts an independent random walk. However, for a fixed integer L ≥ 1, each active particle dies at the instant it reaches a total of L jumps
more » ... l of L jumps without activating any particle. We prove a Law of Large Numbers and a Central Limit Theorem for the proportion of visited vertices at the end of the process.