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

Ugo Bastolla

We examine more in detail the effect of the number of tests for the Italian data in Fig.4 , using the data made available by its Health Ministery [7]. One can see that the number of tests per confirmed cases decreased with time (A), as the consequence both of the saturation of resources and of the decision to test only syntomatic subjects (March 25th), which was probably unfortunate since it left the majority of cases uncovered. As the number of tests decreased, the apparent instantaneous mortality rate D/N increased (B), again in agreement with the linear relationship D/N = δ + α(N/T ). The non-5 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The apparent instantaneous mortality rate D/N increased when the test intensity T /N decreased as D/N = δ + α(N/T ). We report both the non-regularized fit (dashed) and rescaled ridge regression (solid). C: Fraction of confirmed cases that were weak enough to be treated at home versus T /N . D: Estimated fraction of undetected cases versus T /N . regularized linear fit produces the unphysical parameter δ = −0.0136, whereas rescaled ridge regression yields δ = 0.0029 (Fig.4B ). Note that this low instantaneous mortality rate only takes into account those that are already dead at time t and does not consider the extrapolated mortality. Once again, extrapolated to infinite number of tests, data from Italy are consistent with the much lower apparent mortality rates observed in Germany. As the intensity of tests decreased, the fraction of confirmed cases that were weak enough to be treated at home at first decreased and then increased again (Fig.4C) , possibly as the consequence of the almost saturation of the health system that encouraged patients in not too serious conditions to stay at home. Finally, the estimated fraction of undetected cases U increased with decreasing T /N (Fig.4D) . This is of course not surprising, since U is computed from T /N : The aim of the figure is only to quantify the expected impact of reducing the intensity of tests, which appears to be modest.