Undetected infectives in the Covid-19 pandemic

Abstract

Objectives: Epidemiological investigations and mathematical models have revealed that the rapid diffusion of Covid-19 can mostly be attributed to undetected infective individuals who continue to circulate and spread the disease: finding their number would be of great importance in the control of the epidemic.

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-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 undetected infectives, compared to the total number of infected subjects, is given by 1-1R₀, where R₀ is the basic reproduction number. The mean value R₀=2.102.09-2.11 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 of 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 for most of the population.

Keywords: Covid-19; Epidemiology; SARS-CoV-2; SIR model; Undetected cases.