  In networked spreading models, each node can infect its neighbors and cure
spontaneously. The curing is assumed to occur uniformly over time. A pulse
immunization/curing strategy is more efficient and broadly applied to
suppressing spreading processes. We model the epidemic process by the basic
Susceptible-Infected (SI) process with a pulse curing and incorporate the
underlying contact network. The mean-field epidemic threshold of the pulse SI
model is shown to be $\frac{1}{\lambda_1}\ln\frac{1}{1-p}$, where $\lambda_1$
and $p$ are the largest eigenvalue of the adjacency matrix and the fraction of
nodes covered by each curing, respectively. Compared to the extensively studied
uniform curing process, we show that the pulse curing strategy saves about
$36.8$\%, i.e. $p\approx 0.632$, of the number of curing operations invariant
to the network structure. Our results may help related policy makers to
estimate the cost of controlling spreading processes.
