  The SARS-CoV-2 pandemic has necessitated mitigation efforts around the world.
We use only reported deaths in the two weeks after the first death to determine
infection parameters, in order to make predictions of hidden variables such as
the time dependence of the number of infections. Early deaths are sporadic and
discrete so the use of network models of epidemic spread is imperative, with
the network itself a crucial random variable. Location-specific population age
distributions and population densities must be taken into account when
attempting to fit these events with parametrized models. These characteristics
render naive Bayesian model comparison impractical as the networks have to be
large enough to avoid finite-size effects. We reformulated this problem as the
statistical physics of independent location-specific `balls' attached to every
model in a six-dimensional lattice of 56448 parametrized models by elastic
springs, with model-specific `spring constants' determined by the stochasticity
of network epidemic simulations for that model. The distribution of balls then
determines all Bayes posterior expectations. Important characteristics of the
contagion are determinable: the fraction of infected patients that die
($0.017\pm 0.009$), the expected period an infected person is contagious ($22
\pm 6$ days) and the expected time between the first infection and the first
death ($25 \pm 8$ days) in the US. The rate of exponential increase in the
number of infected individuals is $0.18\pm 0.03$ per day, corresponding to 65
million infected individuals in one hundred days from a single initial
infection, which fell to 166000 with even imperfect social distancing
effectuated two weeks after the first recorded death. The fraction of compliant
socially-distancing individuals matters less than their fraction of social
contact reduction for altering the cumulative number of infections.
