A mathematical model is used primarily to establish principles of growth, not necessarily to make predictions. The model depends on the rates of conversion, births, deaths and other such gains and losses from the church. Predictions are possible, but not usually accurate because these rates vary over time. What is possible, however, is to establish principles based on: “if these rates do not change, the church will grow in a particular way.” The model that follows is called the Limited Enthusiasm model, a name based on the model assumptions.
Conversion is a work of God. However, He does use Christians in the conversion of others. They make contact with unbelievers, explaining the gospel to them or bringing them to meetings where that happens. We could call these Christians “enthusiasts”, because they are so enthusiastic for Jesus, their enthusiasm is noticed by others. The early Methodists were called enthusiasts because their zeal impacted the people they met, even though it was initially a derogatory term in their case. At least they were noticed! Not all Christians are such enthusiasts, and even fewer keep this enthusiasm going all their lives.
The model assumes that church growth is driven by such enthusiasts, and that they are only enthusiasts for a limited period of time. Hence the name Limited Enthusiasm model.
An unbeliever gets converted. For a while they are an enthusiast with the fresh zeal of a new convert, still with many unconverted friends. They have caught the "infection" of Christianity.
After a while they settle into church life and their enthusiasm fades. Perhaps they have got too distracted by church life that they have no time for witness. Perhaps they have lost all their non-Christian friends, swapping them for Church ones. Perhaps their friends have become immune to the new convert's enthusiasm. Or maybe the new converts zeal is flagging. Either way they have been "cured of the infection of Christianity, and become a non-contagious Christian.
The church grows through the enthusiasts, but its growth is limited because the faith spreads like an infection. Yes church growth is a disease!
These apply for at most approximately 10 years, the period over which births, deaths and losses can be ignored.
Threshold of revival growth. Growth is similar to an epidemic of a disease. It has small beginnings, which lead to substantial growth, eventually slowing down (figure 1).
Growth ends for lack of contacts, not lack of enthusiasm. The growth eventually ceases because enthusiasts spend proportionally less time "infecting" the shrinking pool of unbelievers. Only if unbelievers are deliberately sought out will growth last.
“Quality” of enthusiasts has more effect than quantity. Spiritual enthusiasm is infectious. A small number of enthusiasts who have something spiritually worthwhile to offer will have more impact than many who have little. This is even more true if they make converts who are as effective as themselves. Replication of enthusiasts is the key.
Substantial growth can come from a small number of enthusiasts. A simulation of the 1904-5 Welsh revival indicates the number of enthusiasts involved in the revival was no more than 2,000 at any one time. Each enthusiast was only responsible for just over one new enthusiast, on average . But that blessing from the Holy Spirit was rapidly passed on to many new converts, making them enthusiasts also. The result was 100,000 conversions in just over a year.
Threshold of extinction. This arises from comparing the church's conversions with the number of losses. Below the threshold there are insufficient conversions to stem its losses, and the church will eventually die, however big its current size.
Starting small doesn't hinder growth. Even the smallest of churches will grow if it converts more than it loses. Even if there are only a few enthusiasts, if their ability to make enthusiasts is above this threshold the church will grow to a limit determined by the rates - it just takes longer to do so.
Improving the conversion rate has more effect than stemming losses. Figure 2 shows a simulation based on UK figures of the 20th century. Note the rise in the proportion of the church enthusiast toward the end of the 20th century. It is typical of a declining church that the proportion of enthusiasts rises, even though their numbers are declining. The 20th century figures indicated that if the pattern continues then the church will slowly head for extinction.
If half of the new converts become enthusiasts the church could recover to 14% of the population by 2100. If all its losses are stemmed it could recover to 24%. However improving the conversion rate by 50% would see the church grow to 35% of the population by 2060 even with all its current losses. The survival and growth of the church is very sensitive to the effectiveness of the enthusiasts.
Using this model how does a church improve its conversion rate? Not just by making more contacts but having more effective contacts - more converts per enthusiast. For this to happen the Christian has to be spiritually transformed, and the heart of the unbeliever must be opened - both of which are in the hands of God. The good news is that He does revive Christians and he does convert those they subsequently come in to contact with. In times of such high infection there is revival - the growth of the Church is dramatic.
 This page is a revised version of an article in Quadrant, September 2000, published by Christian Research. The analysis was conducted in 1999, since then the effectiveness of most denominations has deteriorated, probably because they need to make converts to replace the greater proportion of deaths in an aging church. As such the decline of most denominations has increased. However overall the church is decline is much the same, as the growth of churches in London has to some extent compensated for losses elsewhere.
 Each enthusiasts making "just over one" enthusiast on average, may sound confusing. It means that most made only one enthusiasts, a smaller number made two, a much smaller number made three. Added up it averages to "just over one". The enthusiasts were the people who invited unbelievers to meetings, not the person who took the meeting.
Church Growth - It's a Disease!
The arithmetic of church growth is deceptively simple. Think of a guest service where everybody in the church is asked to bring one new person. What happens to the church’s numbers if all those people came and stay? Clearly the church would double! But what if only some people bring a friend? What if some of those newcomers fall away? It is no longer so simple. This is where mathematics, given certain assumptions, can make precise statements about the church’s growth. A mathematical model is an idealised way of looking at numerical growth .