On the Role of Spatial Effects in Early Estimates of Disease Infectiousness: A Second Quantization Approach

Abstract

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.