Digital Herd Immunity and COVID-19

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

Traditional contact tracing is a multi-stage process. First, one identifies symptomatic, infected individuals. Next, one finds the people they came into close contact with during their infectious period. Finally, one treats or isolates these people before they can go on to infect others. Manual contact tracing becomes difficult for infections that have a period before the onset of symptoms when an exposed person is contagious (the Ω period). Further delay in finding the symptomatic person and their contacts could lead to tertiary infections, making it difficult to control an outbreak. For COVID-19, the incubation period is thought to be around 5-6 days, while the Ω period is estimated to be 1-3 days [2] . The time before becoming contagious, or the latent period L, is around 4 days. Stochasticity of these times aside, it is reasonable to expect that if Ω < L on average, and if the exposed contacts of an individual can be traced before they become infectious, then an epidemic could be prevented. However, the delays typical for manual contact tracing, even just one or two days, can render contact tracing completely ineffective for COVID-19, given the typical L and Ω periods; this conclusion is supported by detailed numerical simulations [5, 12] . This is where digital contact tracing comes in. A smartphone application could enable instant isolation of an infected person and their network of contacts. This halts the transmission chain, because infected contacts cannot infect others during their latent period. The question immediately arises of how widespread such tracing needs to be in order to prevent an epidemic, and this question is the focus of our paper. Below we present a simple model that captures the essential features of disease spread necessary to tackle this problem.