Sideward contact tracing and the control of epidemics in large gatherings

Abstract

Effective contact tracing is crucial to containing epidemic spreading without disrupting societal activities, especially during a pandemic. Large gatherings play a key role, potentially favouring superspreading events. However, the effects of tracing in large groups have not been fully assessed so far. We show that in addition to forward tracing, which reconstructs to whom the disease spreads, and backward tracing, which searches from whom the disease spreads, a third ‘sideward’ tracing is always present, when tracing gatherings. This is an indirect tracing that detects infected asymptomatic individuals, even if they have been neither directly infected by nor directly transmitted the infection to the index case. We analyse this effect in a model of epidemic spreading for SARS-CoV-2, within the framework of simplicial activity-driven temporal networks. We determine the contribution of the three tracing mechanisms to the suppression of epidemic spreading, showing that sideward tracing induces a non-monotonic behaviour in the tracing efficiency, as a function of the size of the gatherings. Based on our results, we suggest an optimal choice for the sizes of the gatherings to be traced and we test the strategy on an empirical dataset of gatherings on a university campus.

Simplicial temporal networks from Wi-Fi data in a university campus: The effects of restrictions on epidemic spreading

“…Also, these quantities can be used to efficiently monitor the different fruition of spaces from distinct classes of users, such as staff and students. Within an approach to epidemic spreading on simplicial temporal networks, using the measured simplex size distribution as an input to the theory, our analysis also provides a specific estimate of the dramatic change in the reproduction number occurring in the total opening phase due to the increasing of contacts [10].…”

“…In the susceptible-infected-recovered (SIR) model on activity-driven simplicial networks [9,10], the interaction network evolves by activating simplices at rate a, the simplex activity; when a simplex (clique) of size s is active, s nodes are chosen uniformly at random to participate in the simplex, producing s (s − 1)/2 interactions. Then, the cluster is destroyed, and the process is iterated.…”

“…We notice that the ratio between the total and partial opening phases is much larger than the ratio between the partial and closing phases. Therefore, while one could imagine controlling the spread with tracing measures in the transition from the closing to the partial opening period [10], the same kind of control would turn out to be ineffective in the transition to the total opening. However, we point out that in the total opening phase, a large percentage of the population had been vaccinated (about 80% in Italy), and the use of the Green Pass (mandatory for the access to the university buildings) implies that only vaccinated or tested people are admitted to the university buildings.…”

“…The basic estimated reproduction number R 0 that we show in Section 3.2 has been evaluated on a temporal network model with simplices in a mean field approach without memory [9,10]. This means that it is assumed that all the s (s − 1)/2 links formed in the group of size s occur between nodes that are always different, with a total reshuffling at each time step.…”

“…The localisation of agents is not as accurate as for GPS and mobile traces [6][7][8], but it can be improved with different tools. Interestingly, Wi-Fi data directly provide the distribution of clusters of users connected to the same access point, potentially crowding the same area and forming temporal simplices which evolve in time [9,10]. This is relevant information to be used as an input for models of of higher order interactions in epidemic and information spreading with complex contagion [11][12][13].…”