Measuring the impact of social-distancing, testing, and undetected asymptomatic cases on the diffusion of COVID-19
Fig 2
Three kinds of connected graphs (the number of nodes = 7 / the sum of degrees = 12) are based on the heterogeneity of networks.
The example network with—(a) high heterogeneity. (b) intermediate heterogeneity. (c) low heterogeneity. The number of links for each node in—(d) the network A. (e) the network B. (f) the network C. The plot (x-axis = the number of links r / the y-axis = the number of nodes with r links) for—(g) the network A. (h) the network B. (i) the network C. There are three kinds of graphs based on the heterogeneity of the networks. If the detection of infected cases connected with detected cases is possible, all susceptible nodes (individuals) in the example network A (on the left side) can be detected for three periods at most. For example, node 2 is detected in period 1. Then, node 1, connected with node 2, can be detected in period 2. Since node 1 is connected with all the other nodes, all the left nodes can finally be detected in period 3. If the first detected node is node 1, all the susceptible nodes can be detected within two periods. However, all susceptible nodes in the example network C (on the right side) can be detected for at least four periods. For example, node 4 is detected in period 1, fortunately. Then, the nodes connected with node 4 (nodes 3 and 5) can be detected in period 2. Similarly, nodes 2 and 6 can be detected in period 3. Finally, nodes 1 and 7 can be detected in period 4. If the first detected node is not node 4, the number of periods required to detect all susceptible cases is more than five.