Mathematical Epidemiology References

The primary model of church growth, the Limited Enthusiasm Model, is similar to the model for the spread of disease. An epidemic is a good analogy for rapid church growth. The enthusiasts are similar to the infected in the SIR epidemic model (SIR = susceptible, infected, removed – the three categories of people involved). Below is a selection of books and papers that have been useful in constructing church growth models, and are part of the mathematical credibility of the project.

Books

  • Anderson R.M. and May R.M. (1987). Infectious Diseases in Humans: Dynamics and Control, OUP.
    Used extensively in the church growth models. Comprehensive account.
  • Bailey N.T.J. (1975). The Mathematical Theory of Infectious Diseases and its Applications, Griffen, London.
    Greater emphasis on mathematics, rather than epidemiology. More appealing to mathematicians.
  • Smith? R.(2008). Modelling Disease Ecology with Mathematics, Institute of Mathematics.
    A more condensed guide to the subject.

Papers

  • Allen, R.F., Heller, K.C. & Pons, M.A. (2022). Analysis of SIR Epidemic Models with Sociological Phenomenon. Spora: A Journal of Biomathematics, 8(1), pp.38-55.
    Mixes epidemiological and social modelling, which became essential to combat COVID.
  • Anderson R.M. (1988). The Epidemiology of HIV Infection, J. Roy. Stat. Soc. A, 151 part 1.
    HIV models use the standard incidence transmission of infection that more closely matches the word of mouth mechanism in the Limited Enthusiasm Model
  • Böttcher L., Woolley-Meza O., Araújo N.A.M., Herrmann H.J., & Helbing D. (2015). Disease-induced resource constraints can trigger explosive pandemics arXiv:1508.05484v1.
    How the impact of an epidemic can affect a population’s ability to control the disease spread, thus creating destructive feedback. The mechanisms discussed have parallels in church growth and decline.
  • Hamer W. H. (1906). Epidemic Disease in England, The Lancet, i, 733-9.
    This early paper describes the “mass action” transmission between two people in the spread of disease.
  • Hethcote H. W. (1994). A Thousand and One Epidemic Models, in Frontiers in Mathematical Biology, ed. S.A. Levin. Berlin: Springer Verlag.
    Describes both the mass action (crowd model), and standard incidence (fixed contacts model) mechanisms of person-to-person transmission in disease. Conversion in the Limited Enthusiasm model generally follows standard incidence, but renewal has density effects and is closer to mass action.
  • Heesterbeek J.A.P. and Metz J.A.J. (1993).The saturating contact rate in marriage and epidemic models, Journal of Mathematical Biology, 31, 529-539.
    Proposed an alternative density-dependent transmission mechanism to the Holling one. Indicates the complexity of reducing mixing and network effects to differential equation and system dynamics models.
  • Kermack W.O. and McKendrick A.G. (1927). A Contribution to the Mathematical Theory of Epidemics, Proc. Roy. Soc., A115, 700-721.
    The first paper on the mathematics of the spread of diseases.
  • Kribs-Zaleta C.M. (2004). To Switch or Taper Off: The Dynamics of Saturation, Mathematical Biosciences, 326, pp 137-142.
    Considers a density-dependent transmission mechanism similar to the Holling term of population biology and the Michaelis-Menten effect of chemical kinetics. The renewal extension to the Limited Enthusiasm model of church growth (Hayward 2010) uses a similar mechanism.
  • May R.M. and Anderson R.M. (1985). Endemic Infections in Growing Populations, Math. Biosciences, 192, pp 137-152.
  • May R.M. and Anderson R.M. (1987). Transmission Dynamics of HIV Infection, Nature, 326, pp 137-142.
  • Raggett G.F. (1982). Modelling the Eyam Plague, Bulletin IMA, 18, pp 221-226.
    A readable account of how the basic epidemic model is applied to real data.