  The pandemic linked to COVID-19 infection represents an unprecedented
clinical and healthcare challenge for many medical researchers attempting to
prevent its worldwide spread. This pandemic also represents a major challenge
for statisticians involved in quantifying the phenomenon and in offering timely
tools for the monitoring and surveillance of critical pandemic parameters. In a
recent paper, Alleva et al. (2020) proposed a two-stage sample design to build
a continuous-time surveillance system designed to correctly quantify the number
of infected people through an indirect sampling mechanism that could be
repeated in several waves over time to capture different target variables in
the different stages of epidemic development. The proposed method exploits the
indirect sampling (Lavalle, 2007; Kiesl, 2016) method employed in the
estimation of rare and elusive populations (Borchers, 2009; Lavall\'ee and
Rivest, 2012) and a capture/recapture mechanism (Sudman, 1988; Thompson and
Seber, 1996). In this paper, we extend the proposal of Alleva et al. (2020) to
include a spatial sampling mechanism (M\"uller, 1998; Grafstr\"om et al., 2012,
Jauslin and Till\`e, 2020) in the process of data collection to achieve the
same level of precision with fewer sample units, thereby facilitating the
process of data collection in a situation where timeliness and costs are
crucial elements. We present the basic idea of the new sample design,
analytically prove the theoretical properties of the associated estimators and
show the relative advantages through a systematic simulation study where all
the typical elements of an epidemic are accounted for.
