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The Epidemics of Donations: Logistic Growth and Power-Laws

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  • Frank Schweitzer
  • Robert Mach

Abstract

This paper demonstrates that collective social dynamics resulting from individual donations can be well described by an epidemic model. It captures the herding behavior in donations as a non-local interaction between individual via a time-dependent mean field representing the mass media. Our study is based on the statistical analysis of a unique dataset obtained before and after the tsunami disaster of 2004. We find a power-law behavior for the distributions of donations with similar exponents for different countries. Even more remarkably, we show that these exponents are the same before and after the tsunami, which accounts for some kind of universal behavior in donations independent of the actual event. We further show that the time-dependent change of both the number and the total amount of donations after the tsunami follows a logistic growth equation. As a new element, a time-dependent scaling factor appears in this equation which accounts for the growing lack of public interest after the disaster. The results of the model are underpinned by the data analysis and thus also allow for a quantification of the media influence.

Suggested Citation

  • Frank Schweitzer & Robert Mach, 2008. "The Epidemics of Donations: Logistic Growth and Power-Laws," PLOS ONE, Public Library of Science, vol. 3(1), pages 1-4, January.
    • Handle: RePEc:plo:pone00:0001458
    DOI: 10.1371/journal.pone.0001458
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    References listed on IDEAS

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    1. Schweitzer, Frank & Zimmermann, Jörg & Mühlenbein, Heinz, 2002. "Coordination of decisions in a spatial agent model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 303(1), pages 189-216.
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    Cited by:

    1. Muñoz, Francisco & Nuño, Juan Carlos & Primicerio, Mario, 2015. "Effects of inspections in small world social networks with different contagion rules," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 76-86.
    2. Pavlin Mavrodiev & Claudio J. Tessone & Frank Schweitzer, "undated". "Quantifying the effects of social influence," Working Papers ETH-RC-13-001, ETH Zurich, Chair of Systems Design.
    3. Wu, Yajing & Guo, Jinzhong & Chen, Qinghua & Wang, Yougui, 2011. "Socioeconomic implications of donation distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4325-4331.
    4. repec:cup:judgdm:v:6:y:2011:i:7:p:616-628 is not listed on IDEAS
    5. Bentley, R. Alexander & Madsen, Mark E. & Ormerod, Paul, 2009. "Physical space and long-tail markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(5), pages 691-696.
    6. Zhigang Cao & Haoyu Gao & Xinglong Qu & Mingmin Yang & Xiaoguang Yang, 2013. "Fashion, Cooperation, and Social Interactions," PLOS ONE, Public Library of Science, vol. 8(1), pages 1-14, January.
    7. Emre Soyer & Robin M. Hogarth, 2011. "The size and distribution of donations: Effects of number of recipients," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 6(7), pages 616-628, October.

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