Statistical Physics of Epidemic on Network Predictions for SARS-CoV-2 Parameters

Abstract

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.