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.

Figure 1

Scheme representing the progression of an individual from the susceptible compartment $S$ to the total infected class $I_{tot}$. The fractions of $I_{tot}$ in the $R$ and $U$ compartments are $\frac{1}{R_0}$ and $1-\frac{1}{R_0}$, respectively.

Figure 2

The fit of the number of removed infectives $R\left(t\right)$ according to the Kermack-McKendrick model in three Italian regions.

Figure 3

Rate $\frac{dR}{dt}$ of newly removed infectives per day according to the Kermack-McKendrick model in three Italian regions.

Figure 4

Comparison between the percentage of undetected infectives obtained using the SIR model and the percentages of asymptomatic infectives in three previous investigations conducted in China, Japan, and Vo' (Italy). The error bars represent the 95% confidence intervals.

Figure 5

Plots against time $t$ of the number of removed, undetected and total infectives in Lombardy, Emilia-Romagna, and Sardinia according to the Kermack-McKendrick model.