Modeling virus spread rate via modern techniques of dimensional analysis

Abstract EN

The ongoing pandemic COVID-19 is caused by a pathogen called SARS-CoV-2 or the novel coronavirus.

The notorious frightening phenomenon of spread of this virus involves many physical variables, and is not amenable to satisfactory analysis via conventional methods.

One simple and accessible way that can determine (at least qualitatively) how virus spread is related to the physical quantities that influence it is that of Dimensional Analysis (DA).

This paper explores the use of a modern approach for Dimensional Analysis in the derivation of dimensionless products related to the virus spread rate.

The derivation is accomplished via the celebrated Gauss-Jordan algorithm, which possesses many obvious advantages for handling linear dependencies and for partitioning variables into basis and regime ones.

The paper utilizes the dimensionless products obtained to build a mathematical model for predicting the speed of virus spread as a function of meteorological and non-environmental variables.

The first cut at the problem fails to find a role for the variables of temperature and humidity, albeit their well-known relevance and importance.

A rigorous remedy is to incorporate more influencing variables of diverse dimensions.

A quick fix, with highly satisfactory results, is obtained here by treating temperature dimensionally as energy, i.e., by assuming that the Boltzmann constant is dimensionless.