I started the church growth modelling project back in 1995 following a chance comment concerning the then-popular “Toronto Blessing”. A friend of mine noted the phenomenon’s growth and said: “It is spreading like a disease!” That got me wondering, could I model the growth in church membership and attendance using the mathematics of the spread of disease? I was particularly interested in the application to Christian revival, especially those in my home country of Wales. I was familiar with mathematical epidemiology, having taught it for twelve years.

After spending a few months working on the model, I produced a report late in 1995[1] and put it up on my university’s website. The internet was new then, but the report was picked up by a number of people and church growth agencies. In particular, it was quoted by Pete Greig in a book called Awakening Cry[2]. He asked me if the report had been published – a comment that inspired me to submit it to a journal and eventually in print in 1999[3].

Paper that kicked off church growth modelling project
The 1999 Church Growth Modelling Paper

Other publications and conference presentations followed[4], and church growth modelling, and its spin-offs, became my research project for the rest of my career. In 2017, a house move caused the project to pause, then one of the spin-off modelling projects took over. Now that I am re-started the church growth project, it is an appropriate time to review progress and think of the future.

Limited Enthusiasm Model

The model developed in 1995 and published in various forms from 1999 onwards is called the Limited Enthusiasm model. An unconverted population are like people susceptible to an infection, with the Christians who make new Christians called enthusiasts, the equivalent of infected people. These enthusiasts do not remain “infectious” forever but eventually become inactive. Church growth ends because the church runs out of enthusiasts, not because it runs out of unconverted people to reach. That church growth was limited by internal factors rather than external factors attracted much interest among church leaders and sociologists of religion[5].

Church growth modelling of the Welsh revival 1904/5. Data fit.
Application of the Limited Enthusiasm Model to the Welsh Revival 1904-5.

Challenging misconceptions about church growth and decline has been an important aspect of the model. Additionally, I have applied the model to specific revivals, estimating their infectiousness, and modelled a range of denominations, categorising behaviour according to expected extinction, stability, or revival[6]. The model has useful for short and medium-term behaviour, although there are too many features missing for time scales of many generations. Nevertheless, the model has provided an appropriate narrative for those who wish to tackle church decline. Some of my predictions on church extinction have also produced reactions among church leaders, especially within Anglican churches[7]!

Other Church Growth Models

I developed various extensions to the Limited Enthusiasm model. For example, there is the renewal process that makes enthusiasts out of inactive Christians is an accelerator of church growth[8]. Similarly, an increase in spiritual life can start revivals[9]. By contrast, institutionalism can oppose growth and bring decline[10]. These and other models are still in a state of development. Publication in academic journals is unlikely as this type of modelling has become less attractive to publishers.

Church growth modelling of Methodist growth and decline Graphs of church numbers and inistitutionalism
Rise and Fall of the GB Methodist Church Due to Institutionalism


There have been four significant spin-offs from the church growth modelling project. Two apply similar ideas in other domains: the spread of minority languages and the dynamics of political party membership[11]. A third area deals with developments in the modelling process using soft variables that model quantities such as Spiritual Life and Institutionalism[12]. This method is essential to give confidence to the above extensions to the church growth models. The final spin-off has been new model analysis methods, the Loop Impact Method, and the Newtonian Interpretative Framework[13]. This latter project has been massive and has impeded my church growth modelling work. Nevertheless, it will be invaluable when interpreting the results of church growth models and weighing up the different factors that cause growth. These latter two spin-offs have benefitted from the System Dynamics methodology pioneered by the late Jay Forrester[14].

Other People’s Work

I am not the only person who does church growth modelling! I have given a list of papers in the reference section[15]. There are not many papers, and few models are developed further. That is par for the course in sociological modelling. However, I have met someone who is investigating church planting movements using mathematics, so hopefully, another person will contribute to the field soon.

The Future

The Church Growth Modelling project came out of my passion for revival in the Christian church. Using the modelling to promote revival and inspire people to seek this work of God must be my priority. Additionally, I want to make the extensions to the church growth models mathematically and academically and provide a model with broader applicability. Finally, I will continue to investigate church decline. However, I hope my emphasis on revival will give hope to churches who wish to reverse their decline.

John Hayward
Church Growth Modelling


  1. Hayward, J.  Mathematical Modelling of Church Growth. Technical Report, UG-M-95-3, 1995.
  2. Greig P. (1998). Awakening Cry. Silverfish.
  3. Hayward, J. Mathematical Modeling of Church Growth, Journal of Mathematical Sociology. 23(4), 255-292, 1999.
  4. Church Growth Modelling Publications.
  5. Limited Enthusiasm Model.
  6. For example, Church of England 2000-2011, Southern Baptist Convention USA 1980-2012, and [7] below.
  7. Anglican Church Decline in the West – The Data; Possible Reasons.
  8. Limited Enthusiasm with Renewal.
  9. Limited Enthusiasm with Spiritual Life.
  10. Institutional Model.
  11. For example, Jeffs R.A., Hayward J., Roach P.A. & Wyburn J. (2016). Activist Model of Political Party Growth. Physica A: Statistical Mechanics and its Applications, 442, 359-372. For others see the  “Non-Church Growth Publications” on the Publications page.
  12. For example, Hayward J., Jeffs R.A., Howells L. & Evans K.S. (2014). Model Building with Soft Variables: A Case Study on Riots. Presented at the 32nd International Conference of the System Dynamics Society, Delft, Netherlands, July 2014
  13. For example, Hayward J. & Roach P.A. (2017). Newton’s Laws as an Interpretive Framework in System Dynamics. System Dynamics Review, 33(3-4), 183-218. See Sociomechanics website.
  14. For more information on this methodology, see the System Dynamics website.
  15. Mathematics of Church Growth References.

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