What proportion of CoV-SARS-2 infected people are asymptomatic?

This is my third attempt to examine this question.  The previous two versions died in draft because the results from various studies were in significant disagreement, so that I could come to no firm conclusion.  Fortunately I have now come across a meta-analysis that should give a clearer answer.  That meta-analysis is by Wenquing He, Grace Yi and Yayuan Zhu, all of the University of Western Otario.  Their paper is "Estimation of the basic reproduction number, averageincubation time, asymptomatic infection rate, and casefatality rate for COVID-19: Meta-analysis andsensitivity analysis" published by medRxiv.

 The results

 As can be seen from He et al's figure 3, the meta-analysis was performed on six studies.  That is not exhaustive as additional studies have been published more or less concurrently with He et al.  He et al find that 46% of infections are asymptomatic.  For comparison, 19.1 (5.2–35.5) of influenza infections are asymptomatic.

He et al also applied a meta-analysis to other key numbers related to the COVID-19 Pandemic.  They found a basic reproduction number (R0) of 3.15 (2.41,3.9), an incubation period of 5.08 (4.77,5.39) days, and a case fatality rate, adjusted for asymptomatic individuals, of 2.72 (1.29, 4.16).

Why does it matter?

Before proceeding to the analysis, it is useful to understand why the proportion of asymptomatic individuals matters.  Essentially, there are two reasons.  Firstly, if the proportion of asymptomatic individuals is high, it becomes harder to detect and control outbreaks of the disease.  That includes new outbreaks that might arise due to the relaxation of social distancing measures.  As a result, knowing the proportion of asymptomatic infections is essential for accurate modelling of the consequences of changes in social distancing rules; and how cautious we should be in relaxing those rules.  Secondly, the proportion of asymptomatic individuals makes a significant difference in modelling the initial outbreak; and understanding how the virus first transferred to humans.

Using He et al's estimate of R0 and incubation period, and on the assumption that in an alert community, even people with mild symptoms will be tested, with 46% of patients being asymptomatic, there is a 99.96% chance a new outbreak will be detected by the generation 2 of the new outbreak (with the originally infected person being generation 0).  In contrast, assuming only patients with severe symptoms are detected, an initial outbreak still has only a 27% chance of being detected in generation 3, ie, 15 days after the first infection, when cumulative infections have risen to 31 people infected.  The latter situation better models the situation for a novel outbreak, when people with mild symptoms will be sent home on the assumption that they only have an unusual presentation of the flu; or potentially not even seek medical help.  In practice, the actual situation is likely to have been intermediate between these two extremes.  It is unlikely that the first infected patient (assuming there was only one) was both symptomatic and had a severe form of the disease.  They are, therefore, quiet likely to never be detected.  (It is also possible they were an animal, with a form of the virus capable of infecting humans.)  The disease is likely to have been detected within the first two to three generations, with retrospective analysis potentially pushing the record of the disease further back.

1) https://www.medrxiv.org/content/10.1101/2020.04.28.20083758v1.full.pdf
2) https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4880086/