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April 2015 On the expected total number of infections for virus spread on a finite network
Antar Bandyopadhyay, Farkhondeh Sajadi
Ann. Appl. Probab. 25(2): 663-674 (April 2015). DOI: 10.1214/14-AAP1007


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 an unit time and the process continues till all infected vertices die out. This model was first studied by [Ann. Appl. Probab. 18 (2008) 359–378]. In this work we find a simple lower bound on the expected number of ever infected vertices using breath-first search algorithm and show that it asymptotically performs better for a fairly large class of graphs than the upper bounds obtained in [Ann. Appl. Probab. 18 (2008) 359–378]. 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 $\beta<\frac{1}{r-1}$.


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Antar Bandyopadhyay. Farkhondeh Sajadi. "On the expected total number of infections for virus spread on a finite network." Ann. Appl. Probab. 25 (2) 663 - 674, April 2015.


Published: April 2015
First available in Project Euclid: 19 February 2015

zbMATH: 1322.60206
MathSciNet: MR3313752
Digital Object Identifier: 10.1214/14-AAP1007

Primary: 05C80, 60K35
Secondary: 60J85, 90B15

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.25 • No. 2 • April 2015
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