## The Annals of Applied Probability

### On the expected total number of infections for virus spread on a finite network

#### Abstract

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 $\beta<\frac{1}{r-1}$.

#### Article information

Source
Ann. Appl. Probab. Volume 25, Number 2 (2015), 663-674.

Dates
First available in Project Euclid: 19 February 2015

http://projecteuclid.org/euclid.aoap/1424355127

Digital Object Identifier
doi:10.1214/14-AAP1007

Mathematical Reviews number (MathSciNet)
MR3313752

Zentralblatt MATH identifier
1322.60206

#### Citation

Bandyopadhyay, Antar; Sajadi, Farkhondeh. On the expected total number of infections for virus spread on a finite network. Ann. Appl. Probab. 25 (2015), no. 2, 663--674. doi:10.1214/14-AAP1007. http://projecteuclid.org/euclid.aoap/1424355127.

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