  We study the following model of disease spread in a social network. At first,
all individuals are either infected or healthy. Next, in discrete rounds, the
disease spreads in the network from infected to healthy individuals such that a
healthy individual gets infected if and only if a sufficient number of its
direct neighbors are already infected. We represent the social network as a
graph. Inspired by the real-world restrictions in the current epidemic,
especially by social and physical distancing requirements, we restrict
ourselves to networks that can be represented as geometric intersection graphs.
We show that finding a minimal vertex set of initially infected individuals to
spread the disease in the whole network is computationally hard, already on
unit disk graphs. Hence, to provide some algorithmic results, we focus
ourselves on simpler geometric graph classes, such as interval graphs and grid
graphs.
