Digital Herd Immunity and COVID-19

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

Top: Phase diagrams of epidemic control for R0 = 3, where the tuning parameters are θ, the rate of asymptomatic transition, and φ, the fraction of contact-tracing app ownership among the population. RS denotes the basic reproduction number for pre-symptomatic transmission. Each phase diagram was generated from 4000 microscopic simulations of 20 generations of disease evolution on 10, 000 nodes, of which 100 nodes were initially infected at random. A black square denotes epidemic control (average growth in the cumulative number of infections over the generations 16 − 20 is less than 0.25% of total population). This is grayscaled continuously to white for late-time growth exceeding 2.5% per generation or full epidemic spread before 20 generations have elapsed. Dashed red curves denote the mean-field approximation to the phase boundary, θ = θc(φ) derived in Sec. II C. The exact critical point for θ = 0 and RS = 2, derived in Appendix A, is marked by a cyan arrow. Bottom: Sample simulations from the encircled region in the RS = 0 phase diagram. Curves (solid) denote cumulative number of infections as a percentage of total population, averaged over 10 samples (dashed), with θ = 0.5 fixed and φ varied from φ = 0.6 to φ = 0.9.