Thursday, 20 November 2014

The Eyam Plague of 1666: A System Dynamics Model

At present the news is full of the rather frightening Ebola outbreaks in West Africa. Other infectious diseases also get into the news often, for example AIDS/HIV and flu. What is less well know is that such infectious diseases spread according to fairly precise mathematical rules. This follows from the person-to-person contact involved in the spread of the disease.

It is this process that the limited enthusiasm hypothesis of the church growth models is based on. In that case the “disease” is faith, and it is spread by word of mouth contact. It is not only churches that grow this way, the same epidemiological mechanism has been used to model the spread of languages, scientific ideas, riot behaviour, bulimia, cigarette smoking and even Facebook [1].

To illustrate how this principle works I want to use a standard case study in mathematical epidemiology: the spread of the plague in the Derbyshire village of Eyam in 1666.

Eyam Plague

The years 1665-1666 saw the great plague hit England, notably London, which lost about 15% of its population [2]. This was the last epidemic of bubonic plague in the UK, a disease that had been an ongoing problem since the days of the Black Death in the 14th century. The primary mechanism of spread of the disease is through the bite of an infected black rat flea. However once established the disease can spread person-to-person, which gave rise to the popular rhyme “Ring a ring of roses, a pocket full of posies, atishoo, atishoo, we all fall down” [3].

Although largely confined to London, an outbreak occurred in the Derbyshire village of Eyam due to a person acquiring the disease from a piece of infected cloth sent from London in 1665. Once the Eyam outbreak took hold in 1666 the local clergyman took the precaution of isolating the village, as best he could, to prevent the spread of the disease. This action of his made it an ideal case study to mathematically model the spread of a disease, as migration could be ruled out as a major mechanism in its spread.

Such a mathematical model of the plague was carried out by GF Raggett [4] using methods based on differential equations. Raggett explained why the spread of the disease in Eyam must have been largely person-to-person rather than rat fleas, as over the period of a year infected rats would have left the area and infected the wider area. No such cases occurred. Using mathematics Raggett then showed how the model predicted the number of deaths due to the epidemic, and demonstrated some important results [5].

What follows is a system dynamics version of Raggett’s work to help explain how a disease spreads without using mathematics. The model is often called the SIR model, after the symbols in the equations, the epidemic model, or the Kermack McKendrick model, after the first people who published it [6].

System Dynamics Model

The model assumes the population of people are split into 3 categories of people: the Susceptibles, who could potentially catch the disease; the Infected, who are carrying the disease and could infect others; and the Removed who have had the disease and cannot catch it again, either because they are cured and immune, or have died. The letters SIR stand for these three categories.

In system dynamics this model can be expressed as stocks and flows:

Figure 1
The removed category has been renamed Deceased as most cases of bubonic plague ended in death.

There are two processes (called flows) involved: catch the disease, which moves susceptibles into infected; and deaths, which moves infected into deceased.

The catch disease process is subject to two social forces: R1 and B1. R1 causes the increase in the number of infected to accelerate as more infected gives more new cases each day, thus more infected. This is called reinforcing feedback and is the first phase of growth in the infected, (figure 2).

Figure 2

In addition the force B1 slows that growth as the pool of susceptibles is depleted, making it harder for infected people to make new cases. This slowing force is balancing feedback and opposes the force R1. B1 eventually dominates over R1, the second phase of growth (figure 2) [7].

Eventually the number who catch the disease drops below the deaths and B1 now causes the infected to decline faster and faster, the first phase of decline (figure 2).

The deaths process is subject the social force B2 as the more infected there are the more die, thus depleting their numbers. This force only dominates at the end causing the decrease in infected to slow down, the second phase of decline, (figure 2).

Raggett [4] showed from the recorded deaths that when the main period of the plague epidemic started, June 19th 1666, there were 7 people infected. The population was known to be 261 at that time. By the end of the epidemic, in the middle of October that year, only 83 people had survived.

From these figures, and knowing the infectious period of the plague is about 11 days, it is possible to simulate the system dynamics model, and compare it with the data for cumulative deaths (green curve, figure 3) [8]. Comparing Deceased with recorded deaths shows a good fit. It is remarkable that something that involves people, and random behaviour, gives such predictable results. This predictability is what allows modern day epidemics to be so successfully tackled, and the consequences of not tacking action computed [9].

Figure 3

Note the following:

1. The epidemic burns out before everyone gets the disease. There are susceptibles remaining at the end of the epidemic (black curve figure 3).

2. At the peak of the epidemic, where the number of daily cases is at a maximum (about 45 days, figure 3), even though the daily death rate is slowing down the epidemic is not at an end and a significant number of deaths are still to come, (green curve figure 3).

3. At any one time the number of infected people is quite small compared with the population (blue curve, figure 2 and figure 3). It is their cumulative number over time that is large. It does not take many infected people at a given time to keep an epidemic going [10].

Reproductive Ratio

The strength of an epidemic is measured by the reproductive ratio, called R0. At its simplest it is the number of people one infected person could potentially infect during their infectious period, if the whole population were susceptible [11]. The number has to be bigger than one for an epidemic to happen. The larger this number then the bigger the epidemic becomes. Different diseases have different reproductive ratios [12].

Using the numbers above, the reproductive ratio comes out at about R0 = 1.6 [13]. This is much less than highly infectious diseases such as Measles (range 12-18) and Smallpox (5-7) [14]. Nevertheless 1.6 was still large enough for well over half the population of Eyam to get the disease. A value of R0 of 1.6 is similar to Ebola (1.5-2.5). However because Bubonic Plague is spread through fleas, and through the air, it is harder to take action to reduce R0 compared with Ebola, which is only spread through contact with bodily fluids.


What turned out to be an ideal case study to test a mathematical model for the spread of a disease turned out to be a tragedy for the people of Eyam. The majority of the population died, including the wife of the brave clergyman who isolated the village and performed all the burials [15]. However his action saved many more lives of people in the region, and the lessons learned, which mathematicians can now explore, gives confidence to models that have given strategies to combat epidemics and save millions of people. That studies of this sort can help understand social diffusion processes such as religion is a bonus.

References & Notes

[1] For a selection of social modelling papers that use the epidemic/disease analogy see references at:

[3]  For a history of the Great Plague of London see Wikipedia and the references contained within.

[4]   Raggett, Graham F. "Modelling the Eyam plague." Bull. Inst. Math. and its Applic 18, no. 221-226 (1982): 530.
Note Raggett used the burial records to estimate deaths. There is a slight time delay between the two, but not enough to seriously affect his results.

[5] For a history of the Eyam plague see:
Wallis, Patrick. "A dreadful heritage: Interpreting epidemic disease at Eyam, 1666–2000." In History workshop journal, vol. 61, no. 1, pp. 31-56. Oxford University Press, 2006.

For the demography of the Eyam plague see:
Race, Philip. "Some further consideration of the plague in Eyam, 1665/6." Local population studies 54 (1995): 56-57.

[6] Kermack, William O., and Anderson G. McKendrick. "Contributions to the mathematical theory of epidemics. Part I." In Proc. R. Soc. A, vol. 115, no. 5, pp. 700-721. 1927.

[7] The structure of the feedback loops, or forces, on those who catch the disease can be broken down into a number of parts where it is assumed the populations are proportionally mixed. The connection between population density and the likelihood of contact requires further assumptions.

[8] The model was constructed and simulated in the Software Stella, available from ISEE Systems

[9] Similar models for Ebola in West Africa, 2014, have already been constructed and are informing policies to reduce its impact. For example:

Meltzer, Martin I., Charisma Y. Atkins, Scott Santibanez, Barbara Knust, Brett W. Petersen, Elizabeth D. Ervin, Stuart T. Nichol, Inger K. Damon, and Michael L. Washington. "Estimating the future number of cases in the Ebola epidemic—Liberia and Sierra Leone, 2014–2015." MMWR Surveill Summ 63, no. suppl 3 (2014): 1-14.

Kiskowski, Maria. "Description of the Early Growth Dynamics of 2014 West Africa Ebola Epidemic." arXiv preprint arXiv:1410.5409 (2014).

Team, WHO Ebola Response. "Ebola virus disease in West Africa—the first 9 months of the epidemic and forward projections." N Engl J Med 371, no. 16 (2014): 1481-95.

[10] All these epidemiological principles are replicated in church growth, and other forms of social diffusion. Not all people in a population are converted. Substantial church growth still comes after the peak in the growth is over. At any one time there are very few infected, called enthusiasts, spreading the faith.

[11]  The reproductive ratio (or reproductive number)  is called the reproduction potential in church growth and measures how many people one enthusiast can potentially convert and make an enthusiast. Not all converts become enthusiasts.

[12] For most diseases the reproductive ratio is given as a range as its value can depend on population density and particular population behaviours. It is believed that Ebola in West Africa in 2014 started with a much higher than normal R0 due the particular burial practices used, allowing dead bodies to transmit the disease, thus extending the infectious period.

[13] A simple formula can be used to compute the reproductive ratio in terms of the population number, and initial and final number of susceptibles alone. This calculation was done in the software Mathcad:

For the computation of this formula for the reproductive ratio see:

Brauer, Fred. "Compartmental models in epidemiology." In Mathematical epidemiology, pp. 19-79. Springer Berlin Heidelberg, 2008.

Brauer, Fred. "Compartmental models for epidemics." (2008).

There are numerous methods to compute the ratio, sometimes giving different answers, see [14] below. This is not an exact science.

Mathcad is available from

[14] Wikipedia and references within.

[15] There is a museum in Eyam where the visitor can learn about the outbreak. Note that there had been cases and deaths in 1665 and early 1666 before the period of study used by Raggett starting June 19 1666. Thus the total deaths, and the original village size, are larger than used in Raggett’s study.

Thursday, 6 November 2014

Is the Charismatic Revival Over?

The Changing Nature of Worship Songs

In a recent article for Christian Today, worship leader Noel Richards passed comment on the style of worship songs written in the 1990s and those written now[1]. His central thesis is that there were songs sung then, especially in the events like March for Jesus, that are not appropriate now. His article was a response to a previous one by Martin Saunders who called for ten 90s worship anthems to be revived, songs such as Called to a Battle and Champion, both Richards’ songs[2].

My intention in this blog is to examine Richards’ claims as evidence for a tentative thesis of mine: that the revival, known as charismatic renewal, which started around 1960, is now over[3]. The thesis is only tentative, as it will take more evidence than presented here to prove it. Up to now it has been a thesis I have alluded to in articles and talks just based on my personal observations.

So to Noel Richards’ article.

Evidence 1

The focus of the movement has shifted from spiritual internals to human externals.

Richards sets his article’s context with this sentence:

The charismatic/evangelical churches were at the cutting edge of worship in those days.

Now I know exactly what he means, I was there at the time, leading worship, sometimes with his songs (thank you Noel!). But I think he has revised history a bit. The charismatic churches were at the cutting edge of a movement where the Holy Spirit transformed people. Worship was part of that movement, but only part. The changes in worship style were an external and human-centred expression of the God-centred and internal work in people’s hearts.

Once people look back and focus on the externals, such as worship, rather than heart changes, such as baptism with the Spirit, then it is a sign that the movement or revival is over. Think how people still praise the wonderful hymns of Wesley from the 18th century. But the Methodist revival was about conversion and being saved, not about the hymns[4]! Only once the conversions ended and the evangelistic, and evangelical, fire went out did people start lauding the hymnology.

Likewise the elevation of worship songs and styles now is a sign that the charismatic revival that spawned them is over. The external has taken over from the internal, the work of man rather than the work of God. Richards says:

We believed that worship and prayer events would help pierce the darkness over our towns and cities.

Not really! We believed that people filled with God’s Holy Spirit would be used by him to pierce the darkness. The events were merely the means to receive from God.

Evidence 2

The movement ceases to be lay and voluntary, but has become the domain of the professional and specialist.

Richards states:

The 1990s saw a generation of pioneering hymn-writers such as Chris Bowater, Graham Kendrick, Dave Fellingham, Dave Bilbrough, Martin Smith.

In reality the true pioneers of the worship of charismatic renewal were in the 1960s and 1970s. People like the Fisher Folk from the Church of the Redeemer Houston[5], or Keith Green. They were a small part of the “worship in the Spirit” pioneers, two of the few who became known as they managed to produce albums and song books. The bulk of the pioneers were not professionals, produced no media, and only achieved local prominence, but they were used by God to transform thousands of lives. History does not record who most of these pioneers were, but they wrote songs that ordinary church people could play, the key dynamic that took worship leading out of the hands of the musical expert and placed it in the hands of the Spirit-filled believer.

What the people mentioned by Richards actually pioneered was the rise of the worship music industry, along with many Vineyard and Calvary Chapel musicians in the USA. Undoubtedly their songs were better written, the musical standards higher, and they have been a huge inspiration to many, but from a Holy Spirit point of view they were building on the work of others now forgotten. Their songs were undoubtedly used by God to pursue the revival, but their legacy now is a worship music genre that is so professional in its standards that it is beyond the reach of all but the best musicians. A complete reversal of the charismatic revival’s origins! [6]

That the worship of charismatic renewal is now firmly in the hands of professionals and focuses on the production of media, such as albums, rather than producing Spirit-filled people, is a sign the revival is over. In sociological terms the “worship song” has been “routinized”, set into a fixed form. What was spontaneous has been codified, almost developed its own liturgy. Worship songs really do sound like “worship songs”, slightly dated versions of modern pop music [7] whose formula can’t be challenged. Revival challenges such things. Thus I conclude the revival is over.

Evidence 3

The movement has become timid and unable to proclaim its message boldly.

A feature of any revival is its willingness to engage with the world, proclaim its message publicly and face the consequences. Think of the origins of Christianity or the Methodist revival in the 1700s. The Holy Spirit drives believers into the open.

Richards says that:

The church and the world of 2014 is very different to that of the 90s.

That is certainly true with regard to the world. There is now far more vocal and organised opposition to Christianity in the West than back in the 1980s. Dare I suggest that some of that opposition is a fruit of the boldness of Christians back in the height of the revival? That rather than seeing the current onslaught on the church by the Western political establishment and non-faith groups as a negative thing, it is actually positive, because at some point the boldness of a Spirit-led movement rattled some cages.

Richards goes on:

Whereas in the 90s I would have been comfortable with the phrase "we are going to take the nation for Jesus", I would not use that language today. Why? How would we feel if a group of people were marching through the streets of the UK singing about taking the nation for Allah?

Another change in the western world has been the demise of widespread protest movements. Gone are the days of the 1960s with student and political demonstrations, and the strikes of the 1970s and early 80s. Such mass challenges to the nation no longer happen as few of the causes have enough enthusiastic supporters to carry it out. By the time Christians took to the streets in March for Jesus, we were about the last ones left! 

Have we forgotten that it is healthy in a free country for ideological groups to publicly challenge a system? That it is actually good for all of us that groups take to the streets saying they want to change the nation? Even groups we do not agree with? Why should Christians be uncomfortable with people singing they want to take the nation for Allah, just because they disagree with it? Could it be that Christians have become uncomfortable with boldness and the certainty of their beliefs, and thus fear such qualities in others? If so that is a sure sign the revival has ended. The change in the content of worship songs away from definitive belief statements that Richards describes also suggests the church has lost confidence in its fundamental message.

It is ironic that as Christians are no longer comfortable with taking the nation for Jesus, humanists are quite comfortable with taking the nation for secular humanism and are very vocal about it. They, and similar “rights” groups, are quite willing to engage in the public arena and influence policy makers and the media to change society into their version of it. They set the agenda for what is politically correct, and lobby to get laws changed, even “laws” that pre-date human history! There is a boldness and revival in humanism and lifestyle ideologies, but it seems there is no longer one in the Christian church.

So I agree with Richards the church of now is not the same as the 1990s, the peak of the charismatic revival. In short it has lost boldness, lost its fighting spirit, and lost the heart of what that revival was about, being saved and filled with the Spirit. Hence I conclude the charismatic revival is over.

Richards asks:

how do people of other faiths and no faith feel, when they hear our militant declarations of Christian dominion?

My guess is they feel the same way I felt in the late 70s when Christians kept telling me about Jesus; offended, irritated and angry. But I am glad they did, I found Jesus! It is never acceptable to society to proclaim Jesus. So when revivals come and society is disturbed by noisy, blunt, uncompromising Christians, rather than apologise for it, accept that this has always been God’s way. Every revival in history has had this effect and always will. It makes revived Christians unpopular with society and often with the church, but it is God’s way. Jesus needs enthusiasts!

Don’t Lament the End of Revival

If the charismatic revival has ended, don’t lament it. Revivals do end. Most end very quickly as they brought rapid changes in individuals, thus spread rapidly and end rapidly. The Welsh revival of 1904 is one such example. A revival that seeks to change churches, as well as individuals, needs time to enact those changes, thus takes longer to spread, so last longer.  But they still end.

The good news is they start again. History, the Bible, and my church growth models show that it only takes a small number of people to receive a fresh move of the Spirit and it will spread and lead to widespread conversions. I can understand why the church is embracing new ways of engaging with society and trying to make itself relevant. But it is a new work of the Holy Spirit and revival that will save the church from its current decline, and save the world, not new methods. In 1960 that revival was only a prayer away, it still is [8].


[1] Christian Today, 30/10/14

[2] Christian Today, 27/10/14

[3] I know not everyone sees the late 20th century charismatic renewal as a revival, but consider the evidence: It was about the Holy Spirit changing people; it spread and transformed mainstream denominations with Holy Spirit ministries; it was behind the Jesus people revival; it spawned many new church movements, notably the UK restoration churches, some of which are still growing; it changed the nature of Pentecostalism; many of the largest congregations today originate in this movement; it is behind the Alpha Course, probably the most successful evangelistic course ever; it has transformed the way churches across the world worship; a high proportion of ordinands for ministry have come from this background. Charismatic renewal as revival needs an article in its own right!

[4] The “Wesley” in “Wesley’s hymns” refers to Charles Wesley. Of course the movement was led by his brother, John, the more famous of the two and the one whose surname gives name to “Wesleyan” as a theology. Charles was also a fine preacher, but his fame is due to his song writing, an important part of the movement, but only a part.

[6] Don’t get me wrong. I really appreciate contemporary worship music. All the songwriters Noel Richards mentioned, and many others, had a huge impact on the charismatic renewal and on many people, myself included. But there is always a danger of the means becoming more important than the end. It happened to hymns, choirs, and even preaching. The same could now be happening with worship music.

[7] Pop music, rock music etc. has also had its movements. It has its periods pioneered by the rank and file, exploding nationally and internationally, only to end in professional routineness. Mass media played a large role in propagating such movements as Rock n Roll, Mersey Beat, Punk and Britpop. But the rise of the Internet, and the vast number of TV and radio channels, has changed the way music is heard and distributed. Together with an extensive back catalogue of songs and styles to access, it is now much harder for new distinctive musical movements to form. As such modern pop music has become quite a mish-mash of styles that is hard for modern worship songs to emulate and stay “modern”. Nevertheless even 2014 worship songs still sound like a “best-of” compilation from an Indie band of 10 years ago!

[7] To read of the beginnings of charismatic renewal as far as mainstream Christianity is concerned read Dennis Bennett, Nine O Clock in the Morning.  Still available new and secondhand.

Tuesday, 2 September 2014

Decline of the Church of England – Update 2001-2012

A year ago I applied the Limited Enthusiasm Model church growth to the decline of the Church of England, based on its published attendance figures 2001-2011 [1]. Since then Statistics for Mission 2012 has been published by the C of E with various updates to figures [2]. This blog aims to analyse the revised C of E data, using the Limited Enthusiasm Model, and see how the predictions have changed.

Recap on Results

In the 2001-2011 analysis I presented two scenarios: an optimistic one, which suggests the C of E starts growing again in the future, about 2030; and a pessimistic one, where the C of E declines slowly to extinction. Attendance data alone is not sufficient to distinguish between the two scenarios; however the underlying cause of the change is the production of enthusiasts, those responsible for conversion and recruitment. If enthusiasts are slowly growing then the optimistic scenarios is more likely, if the are declining then extinction is the more probable result.

Of course it is very hard to count enthusiasts, but it may be possible to measure their other by-products, such as an increase in spiritual activities, community engagement and the like. There are examples of such things in the church, though it is not clear if there are enough.

However the latest findings from the C of E, and some further investigations of the model, suggest caution in thinking there are optimistic scenarios. So what has changed?

1. Attendance 2012

Firstly there is now an extra data point for 2012. This time the Church has decided to revise its way of calculating the “All-Age Weekly Attendance”. This has lead to a downward revision of the numbers since 2008. For data fitting to work the measure of attendance used has to be consistent throughout the whole of 2001-2012. However this is easily corrected and the result is no change at all. Both optimistic and pessimistic scenarios survive

2. Different Measures of Attendance & Membership

The second potentially confounding factor is that the Church computes different measures of “size”. For example there are membership figures, which are the electoral role, not updated every year.  Membership tends to lag attendance in declining churches [3], so not an ideal measure.

There is also adult attendance, Sunday attendance, Easter attendance, highest weekly attendance, usual Sunday attendance and, new in the 2012 report, worshipping community! Confusing? Well there is no simple answer to the question “how many people attend church”. There are regulars and occasionals, but even regulars go on holiday, so on an average count would not give a full a 100% return. Occasional could be anything from once a month to once a year! So multiple measures are needed.

To a modeller it pays to look at all measures, they are measures of slightly different communities. But the Limited Enthusiasm Model can be applied to any type of community, as long as the data is consistently measured over time. The data-fitting is looking for curvature  over time. The right sort of slowing down curvature could indicate growing enthusiasts and a bounce back. So the measure of attendance issue does not change the results.

3. Leaving Rates

This time Statistics for Mission has estimated the number leaving the church, and the number joining. The latter will include those born into the church, and new converts. The reported numbers are not fully consistent as even with death rates they suggest the church is growing, which it is not. But it is likely a number of the “joiners” did so only occasionally, so may not get measured in the All-Age Weekly Attendance figure I am using. All the same extra data is always welcome!

The really interesting result is that the report suggests the leaving rate for the C of E is about 1.25%, significantly lower than I had been using, which was 5%. This sounds like good news, but for my scenarios it is bad news.

It is bad because it means to get an annual 1% annual decline rate there must be less conversions than I had estimated, thus less enthusiasts generated, which pushes the church further below the extinction threshold than I had previously thought. In short there are few optimistic scenarios where the C of E survives. Extinction due to lack of conversions is its likely fate.

A low leaving rate is also bad news as there is less leverage to bring about an improvement. There is less scope to improve retention.

Maybe their figures are wrong. I need to see the same estimates for a few more years to be convinced.

4. Birth and Death Rates

The report also estimates the number of deaths in the church, significantly higher than the national figure, a reflection of the older age profile of the church. By the same token the birth rate in the church will be lower than the national average. In some parishes the birth rate is zero; the biological clock has ticked too far!

The published version of the Limited Enthusiasm Model was not designed to handle this situation – my interest at that time was modelling revival not decline! So I am busy revising the model. But it does mean the C of E is even further below the extinction threshold as it needs to produce even more conversions to make up for its higher death rate and lower biological transmission.

5. Contact with Outside Community

Sadly the most optimistic scenarios in my models, the ones where declining churches turn around, usually come about because the community the church has contact with is growing. Unfortunately this is almost certainly the reverse of the current situation. I suspect the growth is in the communities with no church contact.

It is certainly true that there is growth in the non-Christian community. More people in the 2011 census declared themselves non-Christian compared with 2001. But that should not be assumed to mean they are out of contact with the church, or less likely to be converted and join the church. If the church contacts them at least they will know they are not a Christian rather than just assuming it for cultural reasons as in the past! They may be more likely to convert.

More telling is that the C of E is now too small to contact all the UK population. There are communities, especially rural ones, with no parish churches at all. Additionally there is some evidence that the majority of parishes do not engage in any widespread form of evangelism or witness. What takes place only touches a small part of the wider community [4].

Again I need to revise my models to include the growth of secular, hostile and disconnected communities. But, however it is modelled, it will put the C of E even further below the extinction threshold.


It is difficult to give a positive or optimistic view of the future of the Church of England on the basis of the published data and my models.  Although extinction is a few generations away that is little comfort for a church called to take the gospel to the ends of the Earth and make disciples of all nations. The Kingdom is meant to grow!

But as I said, my models were born in the need to understand revival. Ultimately there is no hope of sustained growth for any church unless it has a God given revival, an outpouring of the Holy Spirit.  The challenge I leave to any reading this blog is not what you will do to tackle church decline, but will you take revival seriously? Will you prayer for revival? Will you convince other Christians of the need for revival? Will you go on praying for the Holy Spirit to come until you are an enthusiast, the type of revived Christian who will sacrifice all to proclaim the gospel, and make converts and disciples for Jesus? Our optimism is in the promises, purpose and power of Jesus Christ!


[1] The Decline of the Church of England, Church Growth Modelling Blog, October 2013

[2] Statistics for Mission 2012, (2014), Archbishops' Council, Research and Statistics, Central Secretariat.

[3] Results of the Membership Model.

[4] Take a random sample of parishes and it is likely you will find an absence of any sort of evangelism course such as Alpha, Christianity Explored, Start and the like. Likewise community engagement projects are either small scale or absent.  

As well as the lack of contact between church and community, I fear the church is not as bold as it was compared with say the late 1980s. Back then we had Marches for Jesus through the streets of Britain. I think most Christians, even Evangelicals, would be too embarrassed to do this now. Hopefully I am wrong.

Wednesday, 13 August 2014

Conversion – Hearts Strangely Warmed

The Meaning of “Conversion” in Church Growth Models

When I present my models on church growth I invariably refer to the process by which a person joins, or starts attending, a church as their conversion. Like the words “believer” and “unbeliever” this often causes some discussion with people, and various suggestions for renaming the conversion process as join, or recruit, etc. The latter are perhaps less threatening as they indicate an outside view of the process, rather than a comment on the inner state of a person’s heart. Nevertheless I stand my ground, and it usually gets me into trouble!

I realise a word like “conversion”, can comes as a threat. The King James  translation of Matt 18:3 says: Except ye be converted, and become as little children, ye shall not enter into the kingdom of heaven. And Acts 3:19: Repent ye therefore, and be converted, that your sins may be blotted out. Pretty blunt stuff! Unless something happens – you are lost. Of course modern translations have eliminated “convert” and replaced it with “turn” or “change”; no doubt more literally correct, but perhaps lacking the profundity of what is required[1].

Of course controversy over the use of the word “conversion” is not new. John Wesley caused a stir when he wrote in his journal, May 24 1738:

In the evening I went very unwillingly to a society in Aldersgate Street, where one was reading Luther’s preface to the Epistle to the Romans. About a quarter before nine, while he was describing the change which God works in the heart through faith in Christ, I felt my heart strangely warmed. I felt I did trust in Christ, Christ alone, for salvation; and an assurance was given me that He had taken away my sins, even mine, and saved me from the law of sin and death.

Although he does not use the word “conversion” here, this event has been described ever after as the moment of his conversion, as stated in the plaque at the spot in Aldersgate Street, figure 1, figure 2. Certainly his journal entry has all the hallmarks of conversion: “change which God works in the heart”, “trust Christ alone for salvation”, “taken away sins”. This journal entry is displayed outside the London Museum on Aldersgate Street, figure 3.
Figure 1: Plaque on the location of John Wesley's Conversion, Postman's Park, Aldersgate Street

Figure 2: Aldersgate Street as it is today

Figure 3: Stone of the Journal Entry of Wesley's Conversion, Near The London Museum

What is more controversial about John Wesley’s conversion is that he was already baptised, confirmed, an ordained minister, been doing works of Christian charity and had even conducted evangelistic campaigns in America. He wrote in his journal January 24 1738: I went to America, to convert the Indians; but oh! who shall convert me? Clearly he believed that even being a minister was no proof of a person being converted.  However, as I hope to show, this is not how I use the word “conversion” in church growth models.

Conversion Model of Church Growth

Consider the following simple system dynamics model of church growth, figure 4:

Figure 4: Conversion Model of Church Growth

The meaning of “conversion” depends on the interpretation of  “believers”, which in turn depends on how the number of believers are measured. For most models two measures are used: either the number of regular attendees at church, using the definition of “regular” relevant to that church; or the number of members of the church, again using the church’s definition of membership. 

If attendance is used, then “conversion” means those start attending in a given year. They are converted in the sense that their Sunday habit has changed. If membership is used then it is their willingness to identify with a church that has changed. They have publicly changed their identity.

Clearly these meanings are not the same as the theological view, which sees conversion as an inner change in the heart. This inner change can happen to church attendees, or church members, not just unbelievers. Thus there may well be unconverted people, in the spiritual sense, in the stock of believers; John Wesley would have been one. Indeed there could be spiritually converted people in the stock of unbelievers, though hopefully only for a temporary period.  There is no attempt, or intention, in the church growth models to model the change in numbers of spiritually converted people; it would be impossible to gain the data necessary to validate the model. Indeed because church people mix together in a different way to the way they mix with those outside church, the system dynamics model of figure 4 would be rendered too simplistic for spiritual conversion[2].

"Conversion" is The Correct Word

Yet there are two senses in which “conversion” is a good word to use for the flow. 

Firstly, the word “conversion” refers to something instantaneous, which is necessary for a flow. Louis Berkof states: conversion in its most specific sense denotes a momentary change and not a process like sanctification. It is a change that takes place once and that cannot be repeated[3]. That is very much the essence of a flow in system dynamics, events that occur at a moment in time. Indeed it is measured as “people converted per year”, but could equally be “people converted per second”, it is that instantaneous.

Of course “seconds” would not be very appropriate as most people cannot pin down the time of their conversion that clearly. It is much easier for people to decide which stock they are in, Unbeliever or Believer, than to give the time at which the change occurred![4]

If instead of using the word “convert” the expression “start attending” were used, then this does not carry the same instantaneous sense, because of the interpretation of regular attendance. Many people start attending gradually; it is an ongoing process, not momentary, thus not a good name for a flow. Likewise “recruit” can be an extended process, in this case carried out by the church through campaigns and the like. “Join” can be treated as instantaneous, the act of having one's name put on a book. But, as the second reason will show, it sends out the wrong message.

There is a second, and more important, reason why “convert” is better than “join”, or “recruit”. The word “convert” leaves open the agency of that change. “Join” implies the agency lies with the person joining – their choice, whereas “recruit” emphasises more the agency of the church in bringing it about – they went out and got them!

I have always intended my church growth models to be as broad as possible, modelling the choice to take up religion by unbelievers, achieved through the action of the church in evangelistic campaigns and witness, empowered by outpourings of the Holy Spirit, or revivals, where the emphasis is on God’s agency in the conversion. If the model tries to tie down the agency in the change from unbelievers to believers too much to any of these three, then it will restrict the understanding and application of the model, and worse, restrict the approach to dealing with church decline.

There are three components in conversion: the demand side of  human agency, activities of the unbelievers in their conversion such as believe, commit, repent; the supply-side of human agency, preaching, evangelism, persuasion; and the Holy Spirit’s agency, the divine-side, new birth, conviction, new life, opened hearts. A model that so ties down the agency as to rule out one or more of those sides is too restrictive. It will set up model boundaries that are narrow and reduce the ability to draw conclusions.

Restrictive Thinking from Narrow Model Boundaries 

An example of this restrictive thinking came about recently in an article in Future First [5] about the perception UK society has of church, Christianity and the like. Not surprisingly the less connected people were with church the more negatively they viewed it, Christians and the things of Christianity.  The article ended by saying that it was deeply troubling that the church’s message of grace appeared to be masked by a perception of judgmentalism, anti-homosexuality, hypocrisy and being old-fashioned.  The writer concluded by saying that the church had much to do to change perceptions and present the unique selling point that no-one else offers, the grace and love of God.

Despite being an interesting and well-researched article, the conclusion to me appears to be too narrow, that the church’s lack of growth results from the way the church presents itself. The focus of the solution was all on the supply of religion by the church, which is inadequate because of the image it portrays. The advice was that the church needs to change its image to one more in tune with society. This is a solely supply-side solution because the problem is perceived as supply-side, the barrier set up by the church to those who wish to join. It has left out the demand-side, that the people’s perception is negative because the people outside need converting! They demand the wrong things. It has left out the divine-side, as it needs God to warm their hearts as much as he did with John Wesley!

Indeed if the church proclaimed its real unique selling point: the death and resurrection of Christ, I would expect there to be more unbelievers with a negative perception of church. The natural man does not receive the things of the Spirit of God, for they are foolishness to him, 1 Cor 2:14. The unbeliever may have no problem with the grace and love of God, many religions have this, it is not unique to Christianity – but it makes no demands. On its own, it reduces church growth to one of  “attract and recruit” rather than “persuade and convert”. The grace and love of God are in the context that people need conversion, the change which God works in the heart through faith in Christ, as John Wesley said. God’s grace and love provided the means to carry this out, historically on the cross, and effectually in the heart by the Holy Spirit.

This is why I always use the word “convert” in my models. They need to encapsulate the three sides of the process of moving from unbelievers to believers: the message the church must supply, which may well incur hostility; what must change in unbelievers’ demand, the desire for God on his terms;  and the work of God which matches the demand with the supply – demand for salvation in  Christ. I like to think that my models can proclaim the gospel as well as model church growth! 

Notes and References

[1] Perhaps modern translations of scripture are translated by academics and scholars, whereas the Authorised/King James version and its immediate precursors was translated by evangelists and pastors? Just a thought!

[2] The difference in mixing within church and without is a matter of the mechanism. Most churches are embedded in large enough communities that the number of contacts a church member makes with unbelievers is limited by the member’s available time, not the size of the community. However Christians form themselves into different churches whose numbers are such that some degree of regular contact and friendship can be maintained. Thus the contact believers have with each other is limited more by the size of their church community, than their available time, unless that church is large. These differences affect the maths; the former is called standard incidence, the latter mass action. The model is described in Church Growth via Enthusiasts and Renewal, 28th International Conference of the International System Dynamics Society, Seoul, South Korea, July 2010

[3] Berkoff  L Systematic Theology, p.485, Banner of Truth,  1988 edition.

[4] There will of course be people who cannot decide which of the two categories they belong to. It would be easy to invent a third category Don’t Know and connect more flows. However as the model is counting membership or attendance then an unsure category is not usually required.

[5] Will Bissett, Perceptions of Those Outside the Church, Future First, No. 34, Brierley Consultancy, August 2014. ISSN 2040-0268.

Tuesday, 4 February 2014

Membership Decline in the Southern Baptist Convention

Every year the new edition of the Yearbook of American and Canadian Churches publishes the membership figures for all the Christian denominations in the USA [1]. Heading up the list of protestant churches is the Southern Baptist Convention (SBC), very much the flagship denomination of Evangelicalism [2]. However, despite a century of strong growth, the SBC has turned a corner and is now showing an annual decline in membership. Decline was once the province of the liberal churches; the conservative ones typified by growth [3]. Not surprisingly such decline in the heartland of American Evangelical Christianity has not gone without note [4].

Back in 2002 I applied the Limited Enthusiasm model [5] of church growth to a number of USA denominations, including the SBC. At that point the model showed that the SBC had experienced the sort of growth associated with revivals, but it had slowed before 2000. The model predicted growth would continue to slow and would be followed in the 2000s by a small decline.  That decline would be a natural phenomenon called overshoot, often seen when there has been previous rapid growth.

Overshoot occurs in a population when it exceeds its natural equilibrium value, often caused by its growth mechanism depending on a smaller subset of the population than that which governs its decline [6]. The subsequent decline ultimately causes the population, the church in this case, to re-balance at its equilibrium value, albeit over timescales of many generations.

The SBC result was published in a paper in 2005 [7]. So with news of that denomination’s actual decline, I was keen to apply the model again to see if the decline matched the predictions. If so, the decline in the SBC could be a temporary re-balancing, rather than the start of a long-term trend.

Membership SBC 1980-2012

To get a sense of perspective I will look at the SBC data from 1980 onwards in comparison to earlier figures.  Figure 1 shows membership from 1950 [8]. The growth of the SBC is impressive, and the decline from 2006 is quite small by comparison. This is not a church that is going to disappear in the next 20 years!

Figure 1: Membership of the SBC from 1950-2012

To get an idea of how much of this growth was making inroads into converting the USA population, the membership figures are compared with the population, expressed as a percentage (figure 2). This graph looks less dramatic, showing that the SBC has been losing ground on a growing population since the 1980s. Its downturn from 2006 is not just a result of factors in the 21st century, but must include the outworking of forces at least 20 years earlier. The SBC should have been growing much faster that it was in the 1970s and 1980s to have been considered a strongly growing denomination.  

Figure 2: Membership of the SBC as a Percentage of the USA Population

That this membership percentage had been rising up to 1980 indicates that conversions were a significant part of its growth prior to that date. There is no evidence that I am aware of that family size among SBC members was significantly larger than the USA norm, the other possible cause.

Before going any further it should be noted that the largest protestant denomination in the USA, the SBC in this case, has never been much more than 6% of the population. The strength of Christianity in the USA lies in its diversity rather than in a single denomination, in marked contrast to European countries.

Data Fitting

To compare the Limited Enthusiasm model with the data, the1980 figure is taken as the starting point. The data fitting technique treats all points equally, so starting earlier will give the past too much priority over recent figures.  As the aim is to see if the decline is a natural outworking of the previous growth the data fitting is stopped in 2006 but the model is allowed to run to 2012 to compare with actual data.

Because some parameters in the model are difficult to estimate, a range of scenarios are produced, based on whether they predict a moderate growth, or a small decline, between 2006 and 2012. Two such scenarios are given in figure 3, and compared with membership figures [9]. All data fits up to 2006 indicate the church is well above the extinction threshold. However it is clear that even the most pessimistic scenario cannot explain the post 2006 downturn.

Figure 3: Limited Enthusiasm Model Compared with SBC Membership 1980-2012

If the cause of the downturn is not overshoot resulting from the prior rapid growth, then what could be its cause? I suggest three:

1.     The leaving rate from the SBC is increasing. If the leaving rate steadily increases from 5% in 2006 to 5.8% in 2012 then this is sufficient to explain the data. A higher leaving rate could be due to members switching to more contemporary churches, or even to more liberal churches; the former being more likely given the even faster decline of the liberal ones.

2.     The ability of the SBC to make converts has been falling. This could be due to a lack of confidence among members of the SBC undermining their witness, or an increasing sense of intimidation by non-Christian society.

3.     The general population is becoming less open to the SBC, whether other Christians who could potentially join, or unbelievers. Either way a greater proportion of non-SBC people are hostile to the SBC.

The decline could be a combination of all three effects [10,11].

If the leaving rate continues to rise, as suggested by the recent data, then the effect on the SBC membership figures will be dramatic (curve 1. figure 4). The church will drop to almost 12 million by 2025, well below its 1980 figure. If the cause is falling conversion rate (curve 2, figure 4), or an increasing hardening rate of potential converts (curve 3, figure 4) the decline is more dramatic, under 12 million by 2025.

Figure 4: Scenarios to Explain SBC Decline


If the SBC is not to see serious decline, the source of its drop in membership figures needs to be identified and dealt with. However the model shows that small changes in the parameters can make significant differences in the numbers in the church, thus there will be realistic measures that will improve the parameters and halt the decline. As the SBC is one of the most successful denominations in the USA, has clear beliefs and a commitment to mission, there seems no reason to believe it will not do what is needed to see more conversions and to keep people in church. As such there is no reason why the pessimistic scenarios of figure 4 should happen, provided action is taken now and not delayed.

References and Notes

[1] The Yearbook of American and Canadian Churches, National Council of Churches, USA.

[2] The 15 Largest Protestant Denominations in the United States, Thom S. Rainer, The Christian Post. March 27 2013.

[3] Why Conservative Churches are Growing: A Study in the Sociology of Religion. Dean Kelley. Mercer University Press, 1986.

[4] The Decline of Evangelical America, John S. Dickerson, The New York Times Sunday Review, 15/12/12.

Southern Baptist Churches Growing in Numbers, Declining in Membership, Marty King,  
Charisma News  6/11/3013 

Southern Baptist ranks decline, once again, Cheryl K. Chumley, The Washington Times, 6/6/13

[5] A description of the Limited Enthusiasm model of church growth is on my website.

[6] The hypothesis of the limited enthusiasm model is that growth is primarily caused by a subset of the population, called enthusiasts, who are responsible for the conversion of those outside the church. Typically enthusiasts are a small proportion of the church. However decline results from people leaving, which affects the whole church, a much larger number of people. Conversion slows when the number of enthusiasts starts dropping, but losses do not drop immediately as the church is still large. Thus the church sees a period of net decline after its rapid growth

Overshoot can also occur if growth is dominated by births rather than conversion. This is a cohort effect due to changing birth rates and the delay between deaths and births.

[7] A General Model of Church Growth and Decline, John Hayward, Journal of Mathematical Sociology, 29(3), pp.177-207, 2005.

[8] Membership figures for the SBC from 2004 are obtained from the Southern Baptist Annual Reports, Earlier figures are obtained from,,  who use a variety of published sources.

[9] For other parameter values see Church Growth Modelling website

[10] There are a number of conditions associated with these results. See Church Growth Modelling website

[11] On a technical note, observe that the down turn in the membership data after the highest point in 2006 is faster, or more curved, then the approach to that point. In social diffusion theory such a turning point is normally explained by a single feedback loop that changes the way it impacts on the population variables; it flips polarity. The result is a symmetrical curve. In the case of the SBC data the down turn is more curved than the growth side, suggesting at least one more process has come into play, possibly another feedback loop. Thus the effect is most likely persistent. Identifying the new processes with certainty would require detailed knowledge of conversion and leaving rates.