Author: Vir Bannerjee Bulchandani; Saumya Shivam; Sanjay Moudgalya; S L Sondhi
Title: Digital Herd Immunity and COVID-19 Document date: 2020_4_18
ID: k8xuv5xy_27
Snippet: To understand the connection between our model and the theory of phase transitions, it it helpful to consider the limit of no contact tracing, i.e. φ = 0, and no pre-symptomatic transmission, R S = 0. In this case, symptomatic individuals act as though they were immune, since they cannot transmit the infection further. Along the line φ = 0, the model exhibits a transition from an "immune phase" to an "epidemic phase" for θ ≥ θ c = 1/R 0 , a.....
Document: To understand the connection between our model and the theory of phase transitions, it it helpful to consider the limit of no contact tracing, i.e. φ = 0, and no pre-symptomatic transmission, R S = 0. In this case, symptomatic individuals act as though they were immune, since they cannot transmit the infection further. Along the line φ = 0, the model exhibits a transition from an "immune phase" to an "epidemic phase" for θ ≥ θ c = 1/R 0 , as shown in Fig. 2 . In fact, when φ = 0 and R S = 0, our model maps exactly to site percolation on a Bethe lattice with coordination number z = 1 + R 0 , where "site percolation" is equivalent to the existence of an infinite cluster of asymptomatic infections. The connection between simple epidemic models and percolation transitions has been noted in the past [20, 21] .
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