  The spread of a contagious disease clearly depends on when infected
individuals come into contact with susceptible ones. Such effects, however,
have remained largely unexplored in the study of epidemic outbreaks. In
particular, it remains unclear how the timing of contacts interacts with the
latent and infectious stages of the disease. Here, we use real-world physical
proximity data to study this interaction and find that the temporal statistics
of actual human contact patterns i) destabilize epidemic outbreaks and ii)
modulate the basic reproduction number. We explain both observations by
distinct aspects of the observed contact patterns. On the one hand, we find the
destabilization of outbreaks to be caused by temporal clustering of contacts
leading to over-dispersed offspring distributions and increased probabilities
of otherwise rare events (zero- and super-spreading). Notably, our analysis
enables us to disentangle previously elusive sources of over-dispersion in
empirical offspring distributions. On the other hand, we find the modulation of
R0 to be caused by a periodically varying contact rate. Both mechanisms are a
direct consequence of the memory in contact behavior, and we showcase a
generative process that reproduces these non-Markovian statistics. Our results
point to the importance of including non-Markovian contact timings into studies
of epidemic outbreaks.
