The Role of Asymptomatic Individuals in the COVID-19 Pandemic via Complex Networks

Background: 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.} Methods: 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. Findings: The proposed model captures an aspect of COVID-19 which is crucial in controlling the further spread of the contagion and in preventing a second wave: \lss{the interactions with undetected cases who have therefore not been isolated}, mostly asymptomatic or paucisymptomatic, namely 1-2 symptoms without anosmia or ageusia, and their impact on latent infections. The evolution of the pandemic is well captured by model fitting with official data from the Protezione Civile, both at a national level as well as regional level. The case study provides insight on the potential effects of localised restrictions, without the coordination at a national level. 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. Interpretation: It is vital to adhere to the prescribed public health measures in order to delay the spread of SARS-CoV-2 and prevent a second wave with potential disruptive national lockdowns. Asymptomatic infected are estimated to be around a third of the official data, but their real number can be much higher if the individuals with one or two minor symptoms are included. The results emphasise the need for coordinated control measures that account for the interactions among different regions in Italy, and potentially among the countries in Europe.} Funding: None.Declaration of Interests: The authors declare no competing interests.