Digital Herd Immunity and COVID-19

Vir Bannerjee Bulchandani; Saumya Shivam; Sanjay Moudgalya; S L Sondhi

By contrast, the non-local structure of recursive contact tracing, as illustrated in Fig. 1 , suggests that the universality class of the immune-to-epidemic transition for φ > 0 is distinct from standard site percolation. Nevertheless, in Appendix A we show that for a population without asymptomatic infections (the line θ = 0 in our phase diagram), we can obtain the critical fraction φ c of app usage exactly, for general values of R 0 , such that an epidemic occurs for φ ≤ φ c and is suppressed for φ > φ c . The calculation proceeds by self-consistently estimating the probability of formation of infinitely long chains of infections, mirroring the standard techniques of percolation theory [22] . In the presence of a finite fraction of asymptomatic people (θ = 0), we rely on a mean-field estimate for the location of the critical line (φ, θ c (φ)) as a function of R S ; detailed studies of the exact location of critical line and the universal features of the contacttracing phase transition are left to future work.