  The way diseases spread through schools, epidemics through countries, and
viruses through the Internet is crucial in determining their risk. Although
each of these threats has its own characteristics, its underlying network
determines the spreading. To restrain the spreading, a widely used approach is
the fragmentation of these networks through immunization, so that epidemics
cannot spread. Here we develop an immunization approach based on optimizing the
susceptible size, which outperforms the best known strategy based on immunizing
the highest-betweenness links or nodes. We find that the network's
vulnerability can be significantly reduced, demonstrating this on three
different real networks: the global flight network, a school friendship
network, and the internet. In all cases, we find that not only is the average
infection probability significantly suppressed, but also for the most relevant
case of a small and limited number of immunization units the infection
probability can be reduced by up to 55%.
