Abstract
Background A crucial role in epidemics is played by the number of undetected infective individuals who continue to circulate and spread the disease. Epidemiological investigations and mathematical models have revealed that the rapid diffusion of Covid-19 can mostly be attributed to the large percentage of undocumented infective individuals who escape testing.
Methods The dynamics of an infection can be described by the SIR model, which divides the population into susceptible (S), infective (I) and removed (R) subjects. In particular, we exploited the Kermack and McKendrick epidemic model which can be applied when the population is much larger than the fraction of infected subjects.
Results We proved that the fraction of undocumented infectives, in comparison to the total number of infected subjects, is given by 
, where R0 is the basic reproduction number. The mean value R0 = 2.10 (2.09 − 2.11) for the Covid-19 epidemic in three Italian regions yielded a percentage of undetected infectives of 52.4% (52.2% - 52.6%) compared to the total number of infectives.
Conclusions Our results, straightforwardly obtained from the SIR model, highlight the role played by undetected carriers in the transmission and spread of the SARS-CoV-2 infection. Such evidence strongly recommends careful monitoring of the infective population and ongoing adjustment of preventive measures for disease control until a vaccine becomes available.
Competing Interest Statement
The authors have declared no competing interest.
Clinical Trial
This study is not a clinical trial.
Funding Statement
The authors received no specific funding for this work.
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Paper in collection COVID-19 SARS-CoV-2 preprints from medRxiv and bioRxiv
The Chan Zuckerberg Initiative, Cold Spring Harbor Laboratory, the Sergey Brin Family Foundation, California Institute of Technology, Centre National de la Recherche Scientifique, Fred Hutchinson Cancer Center, Imperial College London, Massachusetts Institute of Technology, Stanford University, University of Washington, and Vrije Universiteit Amsterdam.
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