Impact of temporal correlations on high risk outbreaks of independent and cooperative SIR dynamics

We first propose a quantitative approach to detect high risk outbreaks of independent and coinfective SIR dynamics on three empirical networks: a school, a conference and a hospital contact network. This measurement is based on the k-means clustering method and identifies proper samples for calculating the mean outbreak size and the outbreak probability. Then we systematically study the impact of different temporal correlations on high risk outbreaks over the original and differently shuffled counterparts of each network. We observe that, on the one hand, in the coinfection process, randomization of the sequence of the events increases the mean outbreak size of high-risk cases. On the other hand, these correlations do not have a consistent effect on the independent infection dynamics, and can either decrease or increase this mean. Randomization of the daily pattern correlations has no strong impact on the size of the outbreak in either the coinfection or the independent spreading cases. We also observe that an increase in the mean outbreak size does not always coincide with an increase in the outbreak probability; therefore, we argue that merely considering the mean outbreak size of all realizations may lead us into falsely estimating the outbreak risks. Our results suggest that some sort of contact randomization in the organizational level in schools, events or hospitals might help to suppress the spreading dynamics while the risk of an outbreak is high.

In Figures 1, 2, 3, 4, 5, 6 we have illustrated the results of the spreading simulations for all networks and their shuffled counterparts for both independent SIR-SIR infection (q = p) and coinfective SIR-SIR (q = 1) cases.
FIG. 1: The results of independent SIR-SIR infection (q = p) simulation on the hospital network, the x axis is the control parameter p, the y axis is the size of the final doubly recovered agents (ab), and the color axis denotes the fraction of realization with the specific value of ab, The gray dashed curve demonstrates the average ρ ab . Please note that the coloring scale is different on each graph, to clarify the discrepancy between different regions of each graph.

FIG. 2:
The results of coinfective SIR-SIR (q = 1) simulation on the hospital network, the x axis is the control parameter p, the y axis is the size of the final doubly recovered agents (ab), and the color code denotes the fraction of realization with the specific value of ab, The gray dashed curve demonstrates the average ρ ab . Please note that the coloring scale is different on each graph, to clarify the discrepancy between different regions of each graph.
FIG. 3: The results of independent SIR-SIR infection (q = p) simulation on the conference network, the x axis is the control parameter p, the y axis is the size of the final doubly recovered agents (ab), and the color code denotes the fraction of realization with the specific value of ab, The gray dashed curve demonstrates the average ρ ab . Please note that the coloring scale is different on each graph, to clarify the discrepancy between different regions of each graph.

FIG. 4:
The results of coinfective SIR-SIR (q = 1) simulation on the conference network, the x axis is the control parameter p, the y axis is the size of the final doubly recovered agents (ab), and the color code denotes the fraction of realization with the specific value of ab, The gray dashed curve demonstrates the average ρ ab . Please note that the coloring scale is different on each graph, to clarify the discrepancy between different regions of each graph.
FIG. 5: The results of independent SIR-SIR infection (q = p) simulation on the primary school network, the x axis is the control parameter p, the y axis is the size of the final doubly recovered agents (ab), and the color code denotes the fraction of realization with the specific value of ab, The gray dashed curve demonstrates the average ρ ab . Please note that the coloring scale is different on each graph, to clarify the discrepancy between different regions of each graph.
FIG. 6: The results of coinfective SIR-SIR (q = 1) simulation on the primary school network, the x axis is the control parameter p, the y axis is the size of the final doubly recovered agents (ab), and the color code denotes the fraction of realization with the specific value of ab, The gray dashed curve demonstrates the average ρ ab . Please note that the coloring scale is different on each graph, to clarify the discrepancy between different regions of each graph.