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Church Growth Modelling

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The Church where I first publicly confessed Jesus Christ as Lord and Saviour.

About Me

My name is John Hayward.

I was a university lecturer in mathematics for 32 years in Wales and Scotland.

I am now a visiting research fellow at my local university. Visit my homepage.

Research Tools

In the project I use a blend of three domains: mathematics, sociology and the Christian faith.

The mathematics tools:

The sociology tools:

The Christian faith tools:

This project aims to glorify the Lord Jesus Christ through assisting in His mission.


Church Growth Modelling is a research project that uses the techniques of mathematical sociology to understand the growth and decline of the Christian Church.

The models give valuable insights into the way the churches grow or decline at either a congregational, denominational, national or international level. They are particularly helpful in describing the dynamics of growth in times of revival.

This website is aimed at church practitioners who wish to understand and enhance the growth of their churches, as well as academics looking for a quantitative understanding of the spread of religion

Origins of Project

The idea that church growth could be modelled with mathematics came to me from two sources. In the early 1990s I was studying, by correspondence, a certificate in Christian studies. One module was on church growth and evangelism. As much as I enjoyed it, and analysed my own church, I was left frustrated that the level of analysis gave me little understanding of how the attendance numbers in my church changed. There was no theory to test the data against.

Then in 1994 the Toronto Blessing occurred. The movement started in Toronto Airport church in January of that year and steady stream of Christians from the UK visited the church to "bring back" the blessing. The movement hit the UK in the summer helped by some media exposure, and particularly the rise of the internet. Someone, not too sympathetic to the movement, made the comment "it is spreading like a disease". That got me thinking. There were well established models for the spread of the disease. Could they be adapted to the growth of a church, especially in times of revival? Although controversial the Toronto Blessing had many of the hallmarks of revival.

I took the standard "SIR" model for spread of disease, reconstructed it to apply to the church. The "infected" Christians became a special category of people who passed on the faith to others. Later I called these enthusiasts after the nickname given to the Methodists in the 18th century. I applied the model to the Welsh Revival of 1904/5 and wrote it up as a technical report for my university in 1995.

The report was widely circulated to a number of Christian agencies and churches. It was even quoted in Pete Greig's Awakening Cry. After comments from people I was encouraged to submit it for publication. I chose the journal of mathematical sociology because of its interest in applications of maths. But I wondered if an application to the things of God was one application too far! I had a very kind anonymous referee who encouraged me to read a number of works on the sociology of religion and then re-submit the paper. Although this took a year to achieve it improved the paper dramatically, and it was published in 1999. Over the years I have had over 400 requests for copies of the paper, many from non-mathematicians.

Since then the model has been extended. I have moved into system dynamics because of its powerful model building capabilities and because it is very presentable to non-mathematicans. Students, both undergraduate and postgraduate, have used the work and applied it to other social phenomena. But it took a move of God in 1994 to start the work off.

It turns out that Lionel Penrose, a statistician, had a similar idea back in 1952, but had not developed it mathematically (Penrose 1953). Also a research group had already applied the epidemic analogy to a different social situation, the spread of riot behaviour, (Burbeck 1978). But I never knew that when I stated my first model. Since the 1990s research in social epidemics has exploded with applications to fashions, crime, the rise of the Internet and persistence of minority languages. A vindication that mathematical modelling can help understand complex human behaviour.

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Church Growth Modelling