How lethal is the novel coronavirus, and how many undetected cases there are? The importance of being tested.

Ugo Bastolla

The pandemic spread of the novel coronavirus SARS-CoV2 is causing thousands of fatalities, creating a tremendous threat to global health [1] . In this situation, the society is strongly concerned by the lethality and the true extension of the pandemics, see for instance [2, 3] . In the media, but also in some non-specialist scientific circles, it is frequent to find that lethality is estimated as the cumulative number of deaths divided by the cumulative number of confirmed cases, data that are easily accessible to everyone in the internet. This quantity changes rapidly and systematically both in time and in space, generating doubts and concerns regarding its interpretation. Of course, epidemiologists can estimate the lethality rate in a less biased way with additional data on the dates in which the infections of the persons that die or recover were detected, and better sampling of the population. However, these data are not easily accessible for all countries. Therefore, here I set up to obtain an estimate of the lethality rate and the detection rate only based on the data reported for all countries in the John Hopkins University database [4] . This extrapolation of the data shows that, when the time course of the disease is controlled for, the lethality estimated for all countries for which reliable data are available depends only on the intensity of the performed tests, i.e. the number of tests divided by the number of positive case. Extrapolating to infinite number of tests, I estimate a lethality rate of 0.012 ± 0.012, which is very noisy but consistent with the estimate of 0.01 that is frequently mentioned in the media. Inverting the relationship between apparent death rate and number of tests, it is possible to estimate that in all countries except South Korea and perhaps Germany, at least at the beginning of the spread, the vast majority of positive cases went undetected, with more than 90 percent undetected cases in some countries such as Italy. These cases that went out of the radar and were not isolated are likely to have contributed strongly to the rapid spread of the virus. Finally, I propose to adopt the ratio between the cumulative number of recovered and the cumulative number of deceased persons, as a potential indicator that can anticipate whether the spread of the epidemics is halting.