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Time evolution of predictability of epidemics on networks

Petter Holme1,2,3,* and Taro Takaguchi4,5

  • 1Department of Energy Science, Sungkyunkwan University, Suwon 440-746, Korea
  • 2Department of Physics, Umeå University, 90187 Umeå, Sweden
  • 3Department of Sociology, Stockholm University, 10961 Stockholm, Sweden
  • 4National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan
  • 5JST, ERATO, Kawarabayashi Large Graph Project, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan

  • *holme@skku.edu
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Phys. Rev. E 91, 042811 – Published 28 April, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.042811

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.

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Phys. Rev. E 91, 042811– Published 28 April, 2015
  • Received 16 December 2014

©2015 American Physical Society

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