Social Diffusion References & Bibliography

Books

The book by Coleman became the definitive volume in mathematical sociology. He put forward models of innovation diffusion which have been extensively investigated since. It is particularly relevant for the church growth models as he proposed the use of the epidemic equations for modelling social diffusion, i.e. the time period of those spreading the phenomena is limited. Bartholomew gives stochastic models of such diffusion.

• Bartholomew DJ (1982), Stochastic Models for Social Processes, Wiley NY. The stochastic approach to dynamical modelling as opposed to the deterministic approach used in the Church Growth Models.
• Coleman JS (1964), Introduction to Mathematical Sociology, The Free Press of Glencoe NY. The foundational work on dynamical models in sociology. Applies diffusion type ideas to the adoption of medical innovations.
• Gilbert N & Troitzsch (1999), Simulation for the Social Scientist, The Open University PA. An overview of a number of simulation approaches to sociological dynamics. Includes a section on system dynamics.
• Weidlich W (2000), Sociodynamics - A Systematic Approach to Mathematical Modelling in the Social Sciences, Dover. A stochastic style of model of a range of social phenomena.

Papers

The most extensively modelled social diffusion phenomena is the diffusion of technological innovations. Such models are also used in marketing. The simplest model is that of Fisher & Pry where, unlike the church growth model, those responsible for spread the innovation do so indefinitely. the well used Bass model is an extension of Fisher-Pry that includes the effects of advertising.

A few applications of diffusion models to other social phenomena exist, but few have been pursued beyond the original basic model.

Spread of Languages

• Baggs I & Freedman HI (1990) A Mathematical Model for the Dynamics of Interactions between a Unilingual and a Bilingual population: Persistence versus Extinction, Journal of Mathematical Sociology, 16(1), 51-75.
• Wyburn J & Hayward J (2008) The Future of Bilingualism: An Application of the Baggs and Freedman Model , Journal of Mathematical Sociology 32(4) Pages: 267-284.
• Wyburn J & Hayward J (2009) OR and Language Planning: Modelling The Interaction Between Unilingual and Bilingual Populations, Journal of the Operational Research Society, 60 (5), 626-636.

Social Disturbance

• Burbeck SL, Raine WJ & Stark MJA (1979), The Dynamics of Riot Growth: An Epidemiological Approach, Journal of Mathematical Sociology, 6, 1-22.
• Crane J, Boccara N, and Higdon K (2000), The Dynamics of Street Gang Growth and Policy Response, Journal of Policy Modelling, 22(1) pp 1-25

Ideas

• Bettencourt L M A, Cintron-Arias A, Kaiser D I, Castillo-Chavez C (2006), The Power of a good idea: Quantitative modelling of the spread of ideas from epidemiological models, Physica A, 364, pp 513-536.

Social Phenomena

• Crane J (1991), The Epidemic Theory of Ghetto's and Neighbourhood Effects on Dropping Out and Teenage Childbearing, The American Journal of Sociology, 96(5), pp 1226-1259
• Lane DC & Husemann E (2004), Movie marketing strategy formation with system dynamics: towards a multidisciplinary adoption/diffusion theory of cinema-going. In: Maier F (ed.) Komplexitat und dynamik als herausforderung fur das management. DUV, pp. 179-222.

Product Diffusion

• Kumar V & Kumar U (1992), Innovation Diffusion: Some New Technological Substitution Models, Journal of Mathematical Sociology, 17(2-3), 175-194. A review of product diffusion focusing on the mathematics.
• Mahajan V, Muller E & Bass FM (1990), New Product Diffusion models in Marketing, Journal of Marketing, 54, 1-26. A review of product diffusion and marketing models focusing on the applications
• Bass F (1969), A New Product Growth Model for Consumer Durables, Management Science, 15(5) (January), pp 215-227. The original paper of the famous Bass model.
• Fisher J and Pry R (1971), A Simple Substitution Model of Technological Change, Technological Forecasting and Social Change, 3, pp 75-88. The original paper of the famous Fisher Pry model.

Theory of Social Diffusion

• Granovetter M & Song R (1983), Threshold Models of Diffusion and Collective Behaviour, Journal of Mathematical Sociology, 9, 165-179. Has the thesis that in a population people have varying rates of susceptibility to adoption of an idea, behaviour etc.
• Granovetter M (1973), The Strength of Weak Ties, American Journal of Sociology 78 (6): 1360–1380. Presents the thesis that weak ties between groups are more influential in social diffusion than the strong ties within groups, because, for example, there is less redundancy in weak ties which open up new groups of susceptible people.