Digital Herd Immunity and COVID-19

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

To place our work in context, the classic quantitative analyses of the efficacy of contact tracing [3, 4] , from before the smartphone era, showed that traditional, manual contact-tracing protocols become useless when the rate of non-symptomatic spreading, θ, is too high. By contrast, app-based approaches allow for "recursive" contact tracing, whereby contacts of contacts can be traced to an arbitrary recursive depth, at no additional cost. The effectiveness of recursive contact tracing has been studied in previous work; mathematically rigorous results exist for purely symptomatic transmission [15, 16] and detailed numerical simulations have been performed that take non-symptomatic transmission into account [17] . Some recent works have provided quantitative estimates for the effectiveness of contact-tracing, both non-recursive and recursive, in the specific context of COVID-19 [5, 6, 12] . Our results should be viewed as complementary to these studies. One comparative advantage of the model that we propose is its simplicity; in particular, it provides a natural starting point for understanding the universal properties of the contact-tracing phase transition.