Figure 5
Correlated flows may determine the growth of the outbreak. Three systems with identical epidemiological parameters and underlying networks (of size \(N=200\)) with identical mean and variance are depicted in the same way as described in Fig. 4. The base scenario (grey) displays no correlation between incoming and outgoing flows at its nodes (\(\Gamma =0\), see Eq. (14)) and shows a negligible variation over time in terms of disease spread. Setting this correlation to a negative value causes the disease to die out in the long term (\(\Gamma = -\, 0.3\), green), while a positive correlation results in a scenario of epidemic growth (\(\Gamma = 0.3\), purple). The effect of this correlation on the mobility flows can be identified from the networks: positively correlated networks favour the existence of nodes with both high incoming and high outgoing flows (darker horizontal and vertical lines tend to intersect at the diagonal), while in negatively correlated networks nodes with high incoming flows generally do not have high outgoing flows and vice-versa (darker horizontal and vertical lines do not intersect at the diagonal). Bottom plot shows the eigenvalues of the Jacobian matrix of the three systems shown in the scenarios (smaller, faded symbols), together with their predicted outliers as given by Eq. (15) (larger, solid symbols).
