  In times of outbreaks, an essential requirement for better monitoring is the
evaluation of the number of undiagnosed infected individuals. An accurate
estimate of this fraction is crucial for the assessment of the situation and
the establishment of protective measures. In most current studies using
epidemics models, the total number of infected is either approximated by the
number of diagnosed individuals or is dependent on the model parameters and
assumptions, which are often debated. We here study the relationship between
the fraction of diagnosed infected out of all infected, and the fraction of
infected with known contaminator out of all diagnosed infected. We show that
those two are approximately the same in exponential models and across most
models currently used in the study of epidemics, independently of the model
parameters. As an application, we compute an estimate of the effective number
of infected by the SARS-CoV-2 virus in various countries.
