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Continual Versus Occasional Spreading In Networks: Modeling Spreading Thresholds In Epidemic Processes

Published: 20 January 2022 Publication History

Abstract

Epidemic processes are widely used as an abstraction for various real-world phenomena - human infections, computer viruses, rumors, information broadcasts, etc. [5, 1, 3]. Under the SIR model (susceptible-infected-removed/recovered) in finite networks, the effective reproduction number, R(), decreases as nodes become infected and removed. Hence, the spread process remains active for a while but eventually dies out (following R < 1, "herd-immunity"). Such threshold phenomena have been observed empirically. In these special days of COVID-19, estimations of the spreadinduced Herd Immunity Threshold (HIT) are a key factor in directing strategic decisions concerning the fight against the pandemic.

References

[1]
S. Banerjee, A. Chatterjee, and S. Shakkottai. Epidemic thresholds with external agents. In IEEE INFOCOM 2014, pages 2202--2210. IEEE, 2014.
[2]
T. Britton, F. Ball, and P. Trapman. A mathematical model reveals the influence of population heterogeneity on herd immunity to sars-cov-2. Science, 369, 2020.
[3]
Y. Lu, M. S. Squillante, and C. Wah Wu. Epidemic-like stochastic processes with time-varying behavior: Structural properties and asymptotic limits. SIGMETRICS Perform. Eval. Rev., 45(3), 2018.
[4]
Y. Oz, I. Rubinstein, and M. Safra. Heterogeneity and superspreading effect on herd immunity. Journal of Statistical Mechanics: Theory and Experiment, 2021(3):033405, 2021.
[5]
R. Pastor-Satorras, C. Castellano, P. Van Mieghem, and A. Vespignani. Epidemic processes in complex networks. Reviews of modern physics, 87(3):925, 2015.
[6]
J. Tavori and H. Levy. Super-spreaders out, super-spreading in: The effects of infectiousness heterogeneity and lockdowns on herd immunity. arXiv preprint arXiv:2101.09188, 2021.

Cited By

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  • (2023)On the Convexity of the Effective Reproduction NumberJournal of Computational Biology10.1089/cmb.2022.037130:7(783-795)Online publication date: 1-Jul-2023
  • (2023)Stochastic epidemic spreading: not all super-spreading processes are born equal, neither all lockdown strategiesStochastic Models10.1080/15326349.2023.220132940:1(38-69)Online publication date: 12-May-2023

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Published In

cover image ACM SIGMETRICS Performance Evaluation Review
ACM SIGMETRICS Performance Evaluation Review  Volume 49, Issue 2
September 2021
73 pages
ISSN:0163-5999
DOI:10.1145/3512798
Issue’s Table of Contents
Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 20 January 2022
Published in SIGMETRICS Volume 49, Issue 2

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Cited By

View all
  • (2023)On the Convexity of the Effective Reproduction NumberJournal of Computational Biology10.1089/cmb.2022.037130:7(783-795)Online publication date: 1-Jul-2023
  • (2023)Stochastic epidemic spreading: not all super-spreading processes are born equal, neither all lockdown strategiesStochastic Models10.1080/15326349.2023.220132940:1(38-69)Online publication date: 12-May-2023

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