  Recent seroprevalence studies have tried to estimate the real number of
asymptomatic cases affected by COVID-19. It is of paramount importance to
understand the impact of these infections in order to prevent a second wave.
This study aims to model the interactions in the population by means of a
complex network and to shed some light on the effectiveness of localised
control measures in Italy in relation to the school opening in mid-September.
The formulation of an epidemiological predictive model is given: the advantage
of using this model lies in that it discriminates between asymptomatic and
symptomatic cases of COVID-19 as the interactions with these two categories of
infected individuals are captured separately, allowing for a study on the
impact of asymptomatic cases. This model is then extended to a structured
nonhomogeneous version by means of the Watts-Strogatz complex network, which is
adopted widely to model societal interactions as it holds the small world
property. Finally, a case study on the situation in Italy is given: first the
homogeneous model is used to compare the official data with the data of the
recent seroprevalence study from Istat; second, in view of the return to school
in mid-September, a study at regional level is conducted. The results of this
study highlight the importance of coordinating the deployment of appropriate
control measures that take into account the role of asymptomatic infections,
especially in younger individuals, and inter-regional connectivity in Italy.
