  With the covid-19 pandemic still ongoing and an enormous amount of test data
available, the lessons learned over the last two years need to be developed to
a point where they can provide understanding for tackling new variants and
future diseases. The SIR-model commonly used to model disease spread, predicts
exponential initial growth, which helps establish the infectiousness of a
disease in the early days of an outbreak. Unfortunately, the exponential growth
becomes muddied by spatial, finite-size, and non-equilibrium effects in
realistic systems, and robust estimates that may be used in prediction and
description are still lacking. I here establish a second quantization framework
that allows introduction of arbitrarily complicated spatial behavior, and I
show that a simplified version of this model is in good agreement with both the
growth of different covid-19 variants in Denmark and analytical results from
the theory of branched polymers. Denmark is well-suited for comparison, because
the number of tests with variant information in early December 2021 is very
high, so the spread of a single variant can be followed. I expect this model to
build bridges between the epidemic modeling and solid state communities. The
long-term goal of the particular analysis in this paper is to establish priors
that allow better early estimates for the infectiousness of a new disease.
