Digital Herd Immunity and COVID-19

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

Several natural questions arise for future work. From a practical standpoint, one worthwhile extension of our model would be to allow for a degree of stochasticity in the basic reproduction number R 0 , for example, by simulating the branching-process model on small-world networks with varying degree per node, which are known to better reflect realistic human contact networks [27, 28] than networks with fixed degree. Indeed, network structure has previously been shown to influence the effectiveness of contact tracing [4, [29] [30] [31] . Meanwhile, an important open problem from the perspective of statistical physics is pinning down the universality class of the contact-tracing transition. Our study of the critical point along the line θ = 0 indicates that techniques from percolation theory are likely to be useful; on the other hand, the non-local character of recursive contact tracing distinguishes it from the percolation transitions that have arisen in related applications [20, 21, 32, 33] , and suggests that the critical exponents at the transition point differ from those of standard site percolation, even on the Bethe lattice. We leave a detailed exploration of these fascinating questions to subsequent studies.