Universal scaling law for human-to-human transmission diseases

Abstract

Due to the COVID-19 pandemic, Susceptible-Infective-Recovered (SIR) models and their variants are in high demand for predicting the number of cases in urban areas. Aiming to correctly use the experience of the epidemic evolution from one local to another, we present an analysis of the transmission rate of COVID-19 as a function of population size at the metropolitan area level for the United States. Contrary to the usual hypothesis in epidemics modeling, we observe that the disease transmissibility scales with the logarithm of the local's population size. The analysis, made possible by a large amount of data available on simultaneous epidemics of the same type, is universal for any human-to-human transmission disease. We present a contact rate scaling theory that explains the results.

Reproduction number projection for the COVID-19 pandemic

“…Conceivably, host social behaviour could be sufficiently similar across all SIPs. In this case, Equation ( 1) is a universal scaling law (independent of social behaviour) and should be compared with Cardoso and Gonçalves' universal scaling law [22] obtained by regression. The UK and USA were selected to increase the likelihood of a successful validation.…”

“…R 0 represents the average number of susceptible people a host infects in a completely susceptible population whilst that host is in its infected state [13,14]. Based on estimates of R 0 for COVID-19's causative agent SARS-CoV2, various categories of predictive [1,[15][16][17][18], forecast [19][20][21] and regression [22][23][24][25] models have been constructed to anticipate healthcare system demand.…”

“…It also replaces Hamer's mass action law with its chemistry precursor -the law of mass action [56]. The latter allows the derivation of a population density-dependent R 0 [22,23,52].…”

“…The local estimate requirement causes delay. Cardoso and Gonçalves [22] propose a form for a universal population sizeor density-dependent scaling law and use regression [119] to determine the parameters for COVID-19. Their approach potentially circumvents the need to estimate local modelling parameters locally.…”

“…Hu et al [214] potentially circumvent Cardoso and Gonçalves' [22] regression's requirement for multiple pre-existing disease centres by repurposing formulae from the kinetic theory of ideal gases to derive population density-dependent contact rates. Hu et al 's contact rates are an alternative to the HI-STR model's law of mass action.…”