Digital contact tracing and network theory to stop the spread of COVID-19 using big-data on human mobility geolocalization
Fig 5
(A) Average size of infected population, M [33], in an outbreak average over all starting nodes in a k-shell as a function of the probability of infection β for a SIR model on the network in Fig 4C during the lockdown. The black is the average value over all the network. The average divides the k-shell contribution to the spreading of the virus in two groups: above and below the average. The 0.5-cores have maximal spreading and the 0.5-shell have minimal spreading. Error bars correspond to a confidence interval of 95%. (B) Optimal percolation analysis performed over the network in Fig 4C during the lockdown in following different attack strategies and their effect on the size of the largest connected component G(q) versus the removal node fraction, q. Nodes are removed (in order of increasing efficiency): randomly (blue); by the highest k-shell followed by high degree inside the k-shell [33]; by highest degree (orange); by collective influence (red) [20]; by the highest generalized k-core (brown) [37]; and by the highest value of betweenness centrality (green) [38, 39]. After each removal we re-compute all metrics. The most optimal strategy among those studied is removing the nodes by the highest value of betweenness centrality. (C)-(D) Effect of removing three high betweenness centrality nodes shown in Fig 5B in the network of Fig 4C. (C) We show the 2-core component of the network after the removal of 12 high betweenness centrality nodes. The red node is the one with the highest betweenness centrality value (next node to remove, 13th) and the blue node is the 14th removal. Different k-cores and k-shell are in different colors. (D) Network k-cores are disintegrated after the removal of the high BC nodes.