Digital Herd Immunity and COVID-19

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

1. An illustrative realization of our branching-process model. a) An in-network asymptomatic person (CA) infects R0 = 3 people, whose category of infection is chosen independently and uniformly subject to parameters θ, the fraction of the population that presents asymptomatic cases, and φ, the fraction of the population using a contact-tracing app. b) A CS infection triggers an alert on the contact network, but the CS person and everybody else in their generation is still able to infect people before the contact network is triggered (while we depict RS = 2, we also simulate more realistic values RS = 0, 1). The arrows show the alerts sent to everyone connected to the CS individual by the contact network. c) Once the alert is sent out, everybody in the contact-networkconnected component of the CS individual can be quarantined immediately (thick circles) without giving rise to further disease spread, since they are in the latent (non-contagious) periods of their infections. Everyone outside the contact network continue to infect people as usual. The "recursive" aspect of such contact tracing corresponds to the arrow going back in time in Fig. (1b) ; the middle branch of infections would be missed by a traditional, non-recursive approach.