  This paper is based on the observation that, during Covid-19 epidemic, the
choice of which individuals should be tested has an important impact on the
effectiveness of selective confinement measures. This decision problem is
closely related to the problem of optimal sensor selection, which is a very
active research subject in control engineering. The goal of this paper is to
propose a policy to smartly select the individuals to be tested. The main idea
is to model the epidemics as a stochastic dynamic system and to select the
individual to be tested accordingly to some optimality criteria, e.g. to
minimize the probability of undetected asymptomatic cases. Every day, the
probability of infection of the different individuals is updated making use of
the stochastic model of the phenomenon and of the information collected in the
previous days. Simulations for a closed community of 10000 individuals show
that the proposed technique, coupled with a selective confinement policy, can
reduce the spread of the disease while limiting the number of individuals
confined if compared to the simple contact tracing of positive and to an
off-line test selection strategy based on the number of contacts.
