  Hard-to-predict bursts of COVID-19 pandemic revealed significance of
statistical modeling which would resolve spatio-temporal correlations over
geographical areas, for example spread of the infection over a city with census
tract granularity. In this manuscript, we provide algorithmic answers to the
following two inter-related public health challenges. (1) Inference Challenge:
assuming that there are $N$ census blocks (nodes) in the city, and given an
initial infection at any set of nodes, what is the probability for a subset of
census blocks to become infected by the time the spread of the infection burst
is stabilized? (2) Prevention Challenge: What is the minimal control action one
can take to minimize the infected part of the stabilized state footprint? To
answer the challenges, we build a Graphical Model of pandemic of the attractive
Ising (pair-wise, binary) type, where each node represents a census track and
each edge factor represents the strength of the pairwise interaction between a
pair of nodes. We show that almost all attractive Ising Models on dense graphs
result in either of the two modes for the most probable state: either all nodes
which were not infected initially became infected, or all the initially
uninfected nodes remain uninfected. This bi-modal solution of the Inference
Challenge allows us to re-state the Prevention Challenge as the following
tractable convex programming: for the bare Ising Model with pair-wise and bias
factors representing the system without prevention measures, such that the MAP
state is fully infected for at least one of the initial infection patterns,
find the closest, in $l_1$ norm, set of factors resulting in all the MAP states
of the Ising model, with the optimal prevention measures applied, to become
safe.
