Probability Distribution of SARS-Cov-2 (COVID) Infectivity Following Onset of Symptoms: Analysis from First Principles

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.

Reanalysis of the top-quark pair hadroproduction and a precise determination of the top-quark pole mass at the LHC

In this study,we calculate the tt pQCD production cross-section at the NNLO and determine the top-quark pole mass from recent measurements at the LHC at the center-of-mass energy √S=13 TeV to a high precision by applying the principle of maximum conformality(PMC).The PMC provides a systematic method that rigorously eliminates QCD renormalization scale ambiguities by summing the nonconformalβcontributions into the QCD coupling constant.The PMC predictions satisfy the requirements of renormalization group invariance,including renormalization scheme independence,and the PMC scales accurately reflect the virtuality of the underlying production subprocesses.By using the PMC,an improved prediction for the tt production cross-section is obtained without scale ambiguities,which in turn provides a precise value for the top-quark pole mass.Moreover,the prediction of PMC calculations that the magnitudes of higher-order PMC predictions are well within the error bars predicted from the known lower-order has been demonstrated for the top-quark pair production.The resulting determination of the top-quark pole mass,m^(pole)_(t)=172.5±1.4 GeV,from the LHC measurement at √S=13 TeV agrees with the current world average cited by the Particle Data Group(PDG).The PMC prediction provides an important high-precision test of the consistency of pQCD and the SM at √S=13 TeV with previous LHC measurements at lower CM energies.