an:06430708
Zbl 1322.60206
Bandyopadhyay, Antar; Sajadi, Farkhondeh
On the expected total number of infections for virus spread on a finite network
EN
Ann. Appl. Probab. 25, No. 2, 663-674 (2015).
1050-5164 2168-8737
2015
j
60K35 60J80 60J85 05C80 92D30
percolation; finite graphs; random \(r\)-regular graphs; virus infections; breath-first search; local weak convergence; susceptible infected removed model
Summary: In this work we consider a simple SIR infection spread model on a finite population of \(n\) agents represented by a finite graph \(G\). Starting with a fixed set of initial infected vertices the infection spreads in discrete time steps, where each infected vertex tries to infect its neighbors with a fixed probability \(\beta\in(0,1)\), independently of others. It is assumed that each infected vertex dies out after a unit time and the process continues till all infected vertices die out. This model was first studied by \textit{M. Draief} et al. [Ann. Appl. Probab. 18, No. 2, 359--378 (2008; Zbl 1137.60051)]. In this work, we find a simple lower bound on the expected number of ever infected vertices using a \textit{breath-first search} algorithm and show that it asymptotically performs better for a fairly large class of graphs than the upper bounds obtained in [loc. cit.]. As a by product, we also derive the asymptotic value of the expected number of the ever infected vertices when the underlying graph is the random \(r\)-regular graph and \(\beta<\frac{1}{r-1}\).
1137.60051