The Role of Asymptomatic Infections in the COVID-19 Epidemic via Complex Networks and Stability Analysis

Italy was the first country to be affected by the COVID-19 epidemic in Europe. In the past months, predictive mathematical models have been used to understand the proportion of this epidemic and identify effective policies to control it, but few have considered the impact of asymptomatic or paucisymptomatic infections in a structured setting. A critical problem that hinders the accuracy of these models is indeed given by the presence of a large number of asymptomatic individuals in the population. This number is estimated to be large, sometimes between 3 and 10 times the diagnosed patients. We focus on this aspect through the formulation of a model that captures two types of interactions-one with asymptomatic individuals and another with symptomatic infected. We also extend the original model to capture the interactions in the population via complex networks, and, in particular, the Watts-Strogatz model, which is the most suitable for social networks. The contributions of this paper include (i) the formulation of an epidemic model, which we call SAIR, that discriminates between asymptomatic and symptomatic infected through different measures of interactions and the corresponding stability analysis of the system in feedback form through the calculation of the \scrR 0 as H\infty gain; (ii) the analysis of the corresponding structured model involving the Watts and Strogatz interaction topology, to study the case of heterogeneous connectivity in the population; (iii) a case study on the Italian case, where we take into account the Istat seroprevalence study in the homogeneous case first, and then we analyze the impact of summer tourism and of the start of school in September in the heterogeneous case.