The Epidemics of Donations: Logistic Growth and Power-Laws

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.

[1]  P. Verhulst.  Recherches mathématiques sur la loi d’accroissement de la population , 1845, Nouveaux mémoires de l'Académie royale des sciences et belles-lettres de Bruxelles.

[2]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .

[3]  T. Schelling.  Hockey Helmets, Concealed Weapons, and Daylight Saving , 1973 .

[4]  F. Bass.  A new product growth model for consumer durables , 1976 .

[5]  Mark S. Granovetter.  Threshold Models of Collective Behavior , 1978, American Journal of Sociology.

[6]  Mark S. Granovetter,et al.  Threshold models of diffusion and collective behavior , 1983 .

[7]  In Ho Lee,et al.  Noisy Contagion Without Mutation , 2000 .

[8]  G. Breeuwsma.  Geruchten als besmettelijke ziekte. Het succesverhaal van de Hush Puppies. Bespreking van Malcolm Gladwell, The tipping point. How little things can make a big difference. London: Little, Brown and Company, 2000 , 2000 .

[9]  V. Eguíluz,et al.  Transmission of information and herd Behavior: an application to financial markets. , 1999, Physical review letters.

[10]  The social organisation of fish schools , 2001 .

[11]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[12]  Heinz Mühlenbein,et al.  Coordination of Decisions in a Spatial Agent Model , 2001, ArXiv.

[13]  A. Tsoularis,et al.  Analysis of logistic growth models. , 2002, Mathematical biosciences.

[14]  Frank M. Bass,et al.  A New Product Growth for Model Consumer Durables , 2004, Manag. Sci..

[15]  A. Grabowski,et al.  Epidemic spreading in a hierarchical social network. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  D. Meadows-Klue.  The Tipping Point: How Little Things Can Make a Big Difference , 2004 .

[17]  Peter Sheridan Dodds,et al.  Universal behavior in a generalized model of contagion. , 2004, Physical review letters.

[18]  B. Zheng,et al.  Two-phase phenomena, minority games, and herding models. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Frank Schweitzer,et al.  Modeling Vortex Swarming In Daphnia , 2004, Bulletin of mathematical biology.

[20]  V Schwämmle,et al.  Different topologies for a herding model of opinion. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.