With the hit of new pandemic threats, scientific frameworks are needed to understand the unfolding of the epidemic. The use of mobile apps that are able to trace contacts is of utmost importance in order to control new infected cases and contain further propagation.
Here we present a theoretical approach [1] that uses both percolation and message--passing techniques to quantify the role of automated contact tracing in mitigating an epidemic wave.
Our approach captures the steady state of the SIR epidemic spreading with contact-tracing and test policies based on the mapping of the process to link percolation. Each individual is assigned a variable indicating the adoption or not of the app. Assuming perfect efficiency of the app, the model is based on the fact that only individuals with the app infected by individuals with the app are not able to spread the disease further is infected (see Figure 1).
Our study goes beyond previous attempts to study the effect of the app by fully capturing the non-linear effects of the dynamics and the phase diagram of the process. Moreover, we show that the adoption of the app by a large fraction of the population increases the value of epidemic threshold, and the best strategy in order to maximally delay the percolation transition is given by targeting the hubs. We use both percolation and message-passing techniques to study the role of contact tracing in mitigating an epidemic wave and we predict analytically the phase diagram of the model in random networks with given degree sequence. The analytical results are compared with extensive Monte Carlo simulations showing good agreement for both homogeneous and heterogeneous networks.
In conclusion, the proposed theoretical framework is able to assess the expected impact of contact-tracing apps in the course of an epidemic capturing the non-linear effect of the spreading dynamics. These results are important to quantify the level of adoption needed for contact-tracing apps to be effective in mitigating an epidemic.
[1] G.Bianconi, H.Sun, G.Rapisardi, A.Arenas, “A message-passing approach to epidemic tracing and mitigation with apps,” (2020), arXiv:2007.05277.