Digital Herd Immunity and COVID-19

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

Numerical simulations of this model were performed on 10, 000 nodes with 100 initial infections; the results are summarized in Fig. 2 . The location of the phase boundaries were verified to be independent of both doubling the system size and doubling the number of samples averaged per point shown on the phase diagram, to within the resolution of the phase diagram. Our numerics are consistent with the hypothesis that for any given fraction of asymptomatic transmission 0 ≤ θ < 1, and any presymptomatic reproduction number 0 ≤ R S ≤ R 0 , there is a critical point φ c (θ), corresponding to the onset of "digital herd immunity": epidemic control occurs for a fraction of app owners φ c (θ) < φ ≤ 1. For realistic COVID-19 parameter values, R 0 = 3, R S = 1 and θ = 0.2 − 0.5 [5, 18] , we find that φ c (θ) = 75% − 95%, illustrating that when both presymptomatic and asymptomatic transmission are taken into account, the rate of app coverage necessary to prevent an epidemic can be rather high. Some practical implications of this point are raised in the final discussion. 1 There are also some higher estimates in the literature, e.g. based on the early epidemic dynamics in Wuhan [19] . Given the greatly increased state of awareness of the disease at this point it seems reasonable to assume that such higher values are not relevant to disease dynamics today.