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 don't have a consistent effect on the independent infection dynamics, and can either decrease or increase this mean. While randomization of the daily pattern correlations has no significant effect on the size of outbreak in either of the coinfection or independent spreading cases. We also observer that an increase in the mean outbreak size doesn't 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 misestimating the outbreak risks. Our results suggest that some sort of randomizing contacts in organization level of schools, events or hospitals might help to suppress the spreading dynamics while the risk of an outbreak is high.