What can the ideal gas say about global pandemics? Reinterpreting the basic reproduction number

Through analysis of the ideal gas, we construct a random walk that on average matches the standard susceptible-infective-removed (SIR) model. We show that the most widely referenced parameter, the “basic reproduction number” (ℛ 0 ), is fundamentally connected to the relative odds of increasing or decreasing the infectives population. As a consequence, for ℛ 0 > 1 the probability that no outbreak occurs is 1 / ℛ 0 . In stark contrast to a deterministic SIR, when ℛ 0 = 1.5 the random walk has a 67% chance of avoiding outbreak. Thus, an alternative, probabilistic, interpretation of ℛ 0 arises, which provides a novel estimate of the critical population density γ/r without fitting SIR models. We demonstrate that SARS-CoV2 in the United States is consistent with our model and attempt an estiamte of γ/r . In doing so, we uncover a significant source of bias in public data reporting. Data are aggregated on political boundaries, which bear no concern for dispersion of population density. We show that this introduces bias in fits and parameter estimates, a concern for understanding fundamental virus parameters and for policy making. Anonymized data at the resolution required for contact tracing would afford access to γ/r without fitting. The random walk SIR developed here highlights the intuition that any epidemic is stochastic and recovers all the key parameter values noted by Kermack and McKendrick in 1927.