  Given the urgent informational needs connected with the diffusion of
infection with regard to the COVID-19 pandemic, in this paper, we propose a
sampling design for building a continuous-time surveillance system. Compared
with other observational strategies, the proposed method has three important
elements of strength and originality: (i) it aims to provide a snapshot of the
phenomenon at a single moment in time, and it is designed to be a continuous
survey that is repeated in several waves over time, taking different target
variables during different stages of the development of the epidemic into
account; (ii) the statistical optimality properties of the proposed estimators
are formally derived and tested with a Monte Carlo experiment; and (iii) it is
rapidly operational as this property is required by the emergency connected
with the diffusion of the virus. The sampling design is thought to be designed
with the diffusion of SAR-CoV-2 in Italy during the spring of 2020 in mind.
However, it is very general, and we are confident that it can be easily
extended to other geographical areas and to possible future epidemic outbreaks.
Formal proofs and a Monte Carlo exercise highlight that the estimators are
unbiased and have higher efficiency than the simple random sampling scheme.
