  In this paper we consider a simple virus infection spread model on a finite
population of $n$ agents connected by some neighborhood structure. Given a
graph $G$ on $n$ vertices, we begin with some fixed number of initial infected
vertices. At each discrete time step, an infected vertex tries to infect its
neighbors with probability $\beta \in (0,1)$ independently of others and then
it dies out. The process continues till all infected vertices die out. We focus
on obtaining proper lower bounds on the expected number of ever infected
vertices. We obtain a simple lower bound, using \textit{breadth-first search}
algorithm and show that for a large class of graphs which can be classified as
the ones which locally "look like" a tree in sense of the \emph{local weak
convergence}, this lower bound gives better approximation than some of the
known approximations through matrix-method based upper bounds derived by
Draief, Ganesh and Massoulie in 2008.
