Kurtz, Thomas G.; Lebensztayn, Elcio; Leichsenring, Alexandre R.; Machado, Fábio P. Limit theorems for an epidemic model on the complete graph. (English) Zbl 1160.60334 ALEA, Lat. Am. J. Probab. Math. Stat. 4, 45-55 (2008). Summary: 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 \(L\geq 1\), each active particle dies at the instant it reaches a total 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. Cited in 16 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60F05 Central limit and other weak theorems 60J27 Continuous-time Markov processes on discrete state spaces 92D30 Epidemiology Keywords:epidemic model; random walk; complete graph; Markov chains; law of large numbers; central limit theorem PDFBibTeX XMLCite \textit{T. G. Kurtz} et al., ALEA, Lat. Am. J. Probab. Math. Stat. 4, 45--55 (2008; Zbl 1160.60334)