Abstract
Epidemic outbreaks of new pathogens, or known pathogens in new populations,
spread fear much because they are hard to predict. For theoretical models of
disease spreading, on the other hand, quantities characterizing the outbreak
converge to deterministic functions of time. Our goal in this paper is to shed
some light on this apparent discrepancy. We measure the diversity of (and,
thus, the predictability of) outbreak sizes and extinction times as functions
of time given different scenarios of the amount of information available. Under
the assumption of perfect information -- i.e. knowing the state of each
individual with respect to the disease -- the predictability decreases
exponentially, or faster, with time. The decay is slowest for intermediate
values of the per-contact transmission probability. With a weaker assumption on
the information available, assuming that we know only the fraction of currently
infectious, recovered or susceptible individuals, the predictability also
decreases exponentially most of the time. There are, however, some peculiar
regions in this scenario where the predictability decreases. In other words, to
predict its final size with a given accuracy, we would need increasingly much
information about the outbreak.
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