Time evolution of predictability of epidemics on networks

TL;DR

This paper investigates how the predictability of epidemic outbreaks on networks evolves over time under different information scenarios, revealing exponential decay in predictability and highlighting the impact of information availability.

Contribution

It provides a novel analysis of the temporal evolution of epidemic predictability considering varying levels of information about the outbreak.

Findings

Predictability decreases exponentially over time under perfect information.

Intermediate transmission probabilities slow down the decay of predictability.

Reduced information scenarios also show exponential decay, with some regions where predictability unexpectedly decreases.

Abstract

Epidemic outbreaks of new pathogens, or known pathogens in new populations, cause a great deal of fear 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 more information about the outbreak.