TITLE:
Probability Distribution of SARS-Cov-2 (COVID) Infectivity Following Onset of Symptoms: Analysis from First Principles
AUTHORS:
Mark P. Silverman
KEYWORDS:
COVID, SARS-Cov-2, Period of Infectivity, Probability of Infectivity, Viral Shedding, Infectiousness, Kaplan-Meier Curve, Principle of Maximum Entro-py
JOURNAL NAME:
Open Journal of Statistics,
Vol.13 No.2,
April
27,
2023
ABSTRACT: The phasing out of protective measures by governments and public health
agencies, despite continued seriousness of the coronavirus pandemic, leaves
individuals who are concerned for their health with two basic options over which they have control: 1) minimize risk of
infection by being vaccinated and by wearing a face mask when
appropriate, and 2) minimize risk of transmission upon infection by
self-isolating. For the latter to be effective, it is essential to have an
accurate sense of the probability of infectivity as a function of time following the onset of symptoms.
Epidemiological considerations suggest that the period of infectivity
follows a lognormal distribution. This proposition is tested empirically by
construction of the lognormal probability density function and cumulative
distribution function based on quantiles of infectivity reported by several
independent investigations. A comprehensive examination of a prototypical ideal clinical study, based on general
statistical principles (the Principle of Maximum Entropy and the Central
Limit Theorem) reveals that the probability of infectivity is a lognormal
random variable. Subsequent evolution of
new variants may change the parameters of the distribution, which can be
updated by the methods in this paper, but the form of the probability function
is expected to remain lognormal as this is the most probable distribution
consistent with mathematical requirements and available information.