Slightly Generalized Contagion: Unifying Simple Models of Biological and Social Spreading

  • Peter Sheridan DoddsEmail author
Part of the Computational Social Sciences book series (CSS)


We motivate and explore the basic features of generalized contagion, a model mechanism that unifies fundamental models of biological and social contagion. Generalized contagion builds on the elementary observation that spreading and contagion of all kinds involve some form of system memory. We discuss the three main classes of systems that generalized contagion affords, resembling: simple biological contagion; critical mass contagion of social phenomena; and an intermediate, and explosive, vanishing critical mass contagion. We also present a simple explanation of the global spreading condition in the context of a small seed of infected individuals.


  1. 1.
    Bass F (1969) A new product growth model for consumer durables. Manage Sci 15:215–227CrossRefGoogle Scholar
  2. 2.
    Castillo-Chavez C, Song B (2003) Models for the transmission dynamics of fanatic behaviors, vol 28. SIAM, Philadelphia, pp 155–172Google Scholar
  3. 3.
    Daley DJ, Kendall DG (1964) Epidemics and rumours. Nature 204:1118CrossRefADSGoogle Scholar
  4. 4.
    Daley DJ, Kendall DG (1965) Stochastic rumours. J Inst Math Appl 1:42–55MathSciNetCrossRefGoogle Scholar
  5. 5.
    Dodds PS, Watts DJ (2004) Universal behavior in a generalized model of contagion. Phys Rev Lett 92:218701CrossRefADSGoogle Scholar
  6. 6.
    Dodds PS, Watts DJ (2005) A generalized model of social and biological contagion. J Theor Biol 232:587–604. MathSciNetCrossRefGoogle Scholar
  7. 7.
    Dodds PS, Harris KD, Danforth CM (2013) Limited imitation contagion on random networks: chaos, universality, and unpredictability. Phys Rev Lett 110:158701CrossRefADSGoogle Scholar
  8. 8.
    Gleeson JP, O’Sullivan KP, Baños RA, Moreno Y (2016) Effects of network structure, competition and memory time on social spreading phenomena. Phys Rev X 6(2):021019Google Scholar
  9. 9.
    Goffman W, Newill VA (1964) Generalization of epidemic theory: an application to the transmission of ideas. Nature 204:225–228CrossRefADSGoogle Scholar
  10. 10.
    Granovetter MS, Soong R (1983) Threshold models of diffusion and collective behavior. J Math Sociol 9:165–179CrossRefGoogle Scholar
  11. 11.
    Granovetter MS, Soong R (1986) Threshold models of interpersonal effects in consumer demand. J Econ Behav Organ 7:83–99CrossRefGoogle Scholar
  12. 12.
    Granovetter M, Soong R (1988) Threshold models of diversity: Chinese restaurants, residential segregation, and the spiral of silence. Sociol Methodol 18:69–104CrossRefGoogle Scholar
  13. 13.
    Harris KD, Payne JL, Dodds PS (2014) Direct, physically-motivated derivation of triggering probabilities for contagion processes acting on correlated random networks.
  14. 14.
    Kermack WO, McKendrick AG (1927) A contribution to the mathematical theory of epidemics. Proc R Soc Lond A 115:700–721CrossRefADSGoogle Scholar
  15. 15.
    Kermack WO, McKendrick AG (1927) A contribution to the mathematical theory of epidemics. III. Further studies of the problem of endemicity. Proc R Soc Lond A 141(843):94–122CrossRefADSGoogle Scholar
  16. 16.
    Kermack WO, McKendrick AG (1927) Contributions to the mathematical theory of epidemics. II. The problem of endemicity. Proc R Soc Lond A 138(834):55–83CrossRefADSGoogle Scholar
  17. 17.
    Murray JD (2002) Mathematical biology, 3rd edn. Springer, New YorkzbMATHGoogle Scholar
  18. 18.
    Schelling TC (1971) Dynamic models of segregation. J Math Sociol 1:143–186CrossRefGoogle Scholar
  19. 19.
    Schelling TC (1978) Micromotives and macrobehavior. Norton, New YorkGoogle Scholar
  20. 20.
    Strogatz SH (1994) Nonlinear dynamics and chaos. Addison Wesley, ReadingGoogle Scholar
  21. 21.
    Watts DJ (2002) A simple model of global cascades on random networks. Proc Natl Acad Sci 99(9):5766–5771MathSciNetCrossRefADSGoogle Scholar
  22. 22.
    Watts DJ, Dodds PS (2007) Influentials, networks, and public opinion formation. J Consum Res 34:441–458CrossRefGoogle Scholar
  23. 23.
    Watts DJ, Dodds PS (2009) Threshold models of social influence. In: Hedström P, Bearman P (eds) The Oxford Handbook of analytical sociology. Oxford University Press, Oxford, chap 20, pp 475–497Google Scholar
  24. 24.
    Watts DJ, Muhamad R, Medina D, Dodds PS (2005) Multiscale, resurgent epidemics in a hierarchcial metapopulation model. Proc Natl Acad Sci 102(32):11157–11162CrossRefADSGoogle Scholar
  25. 25.
    Weng L, Flammini A, Vespignani A, Menczer F (2012) Competition among memes in a world with limited attention. Nat Sci Rep 2:335CrossRefADSGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Vermont Complex Systems Center, Computational Story Lab, the Vermont Advanced Computing Core, Department of Mathematics and StatisticsThe University of VermontBurlingtonUSA

Personalised recommendations