small logo

Church Growth Modelling

What's New | About | Contact

Model Results

Principles of Church Growth

Principles of Church Decline

Church of England 2001-2012

Southern Baptist 1980-2012

Related Models

Limited Enthusiasm

Conversion through enthusiasts, the growth mechanism at the core of the demographics model.


Allows for enthusiasts to be made from existing inactive believers.

Spiritual Life

Enthusiasts can build the spiritual life of the church, which in turn improves their effectiveness


Adding migration investigates revival in growing communities


Separating attendance from membership to investigate their correlation with growth and decline.

Aging and Church Decline

Aging effects the Demographics model if the church is in steep decline. Thus corrections are needed.

Simulate Online

Limited Enthusiasm with Demographics

Church of England 1979-1998

UK New Churches 1990-2000

Limited Enthusiasm with Demographics

Births, Deaths, Reversion and Secularisation

The central hypothesis of the limited enthusiasm model is that conversion growth in the church is driven by a sub-group of church members called enthusiasts. See Limited Enthusiasm Model for full description. The analogy is with the spread of a disease, where the enthusiasts are "infected" believers passing the faith on to unbelievers who catch the "disease" of religion.

In addition the demographics model includes births, deaths and reversion, allowing for church decline through, lack of child retention, aging and people leaving the church. The unbelievers are split into those open to conversion and those hardened, allowing for secularisation in society.

The model predicts two thresholds, one of revival-growth which depends on the size of the community that remains unconverted, and one of extinction, that depends on conversion and loss rates. If the potential for enthusiasts to reproduce themselves is over the revival threshold then rapid growth results. If the threshold is under the extinction threshold then the church will eventually decline to zero.


The model consists of four groups of people: enthusiasts who are responsible for spreading the faith, and inactive believers, who both make up the church; open unbelievers who are open to conversion, and hardened unbelievers, make up the rest of society who are outside the church. The hardened unbelievers include those who are antipathetic or hostile to Christianity, open believers who have secularized, or believers who have turned away from church either by abandoning the faith or being hurt.

For simplicity all church members are assumed to be believers and vice versa. This is because there is no data on who among a church membership are true believers in Jesus Christ, and little prospect of it being reliably obtained.

It is further assumed that members are identical with the attendees of the church. This is because there are only reliable data for attendance. Membership data is less reliable as different denominations and churches use different definitions of membership. Thus the model is dealing with attendance and recruitment issues only. Sometimes membership data needs to be used because no attendance data is available.

In reality there will be members and attendees who are not believers, members who do not attend and attendees who are not members. There may even be believers who are neither members or attendees. However these effects will tend to cancel each other out and the above assumptions imply that their net effect is negligible.

The dynamic hypotheses are:

Dynamic Hypothesis

Conversion Through Enthusiasts (R) Enthusiasts are responsible spreading the faith, i.e. conversion to the church. The more they convert the more enthusiasts. This accelerates growth. Spreading the faith can be by many means.
Loss of Enthusiasm (B2) After a period of time the enthusiasts lose their potential to convert. This slows and limits growth.
Diminishing Susceptible Pool (B1) As people are converted the effectiveness of the enthusiasts on the remaining unbelievers become less as proportionally more of the enthusiast's time is spent on believers. This slows growth.
Not All Converts Become Enthusiasts Not every convert becomes an enthusiast. Some become immediately inactive.
Enthusiasts inactive believers leave the church (B3) and become open unbelievers open to rejoining the church (R2). The reasons for leaving are not important, but could include varying commitment, pressures on time, switching denominations or geographical movement. Thus recycling, R2, is possible.
Enthusiasts inactive believers revert, i.e. leave the church and become hardened unbelievers, not open to rejoining. The reasons for reversion may be abandoning the faith, or being hurt by the church, in varying degrees
Hardened unbelievers may become open after a time, and open unbelievers may become hardened. Both softening and hardening processes may be due to actions of the church in society, or actions in society independent of the church such as wealth or poverty. They are fixed rates in this model. Hardening can include secularisation.
All populations have births, but children may change to a different population group before adulthood. For example some children brought up in church become believers, some drift and become open unbelievers, and some dislike religion and become hardened. Likewise children of open unbelievers may become harder than their parents, secularisation; and children of hardened unbelievers may become softer as they do not have the same baggage in their background.
Hardened unbelievers may become open after a time, and open unbelievers may become hardened. Both softening and hardening processes may be due to actions of the church in society, or actions in society independent of the church such as wealth or poverty. They are fixed rates in this model.

Flows and Causal Loops

Unbelievers convert to believers through contact with enthusiasts who have "spread the faith" to them. Some new converts become enthusiasts whereas some become inactive believers. Enthusiasts only remain active for a limited length of time before becoming inactive and taking no further part in spreading the faith. Both types of believers may leave the church and be open to joining again; or revert and be hardened to rejoining.

system dynamics model of limited enthusiasm demographics

The hypotheses can be expressed as a causal loop diagram, where the loops R1, R2, B1 - B3 represent some of the feedback in the system dynamics model:

causal loop diagram of limited enthusiasm demographics

Growth is driven by the reinforcing loop R where enthusiasts are reproducing themselves through conversion. The feedback: more enthusiasts, more conversions, more enthusiasts, gives exponential growth. Growth is opposed by B1, which reduces conversions thus slowing the exponential growth. When conversions have been reduced below the number who lose enthusiasm, B2, the number of enthusiasts starts to decline, and thus church growth slows and eventually halts.

B3 controls the unbelievers who leave the church and are open to rejoining. Thus once revival growth is over the church may decline rather than plateau. A similar loop, not shown, governs the enthusiasts who leave the church. Because of the rejoining effect there is a reinforcing loop from recycling, which helps the church to survive. There are balancing loops associated with reversion, those who leave the church and are not open to rejoining, the hardened unbelievers. If they soften then some may become open in the future giving recycling.

A balancing loop controls open unbelievers becoming hardened (not shown), the effect of secularisation. The model includes loops to control births, and how many remain in the population they were born into. This can contribute to church decline and secularisation. All populations groups have loops for deaths.

What is Meant by "Spreading the Faith"?

All aspects of conversion and spreading the faith are discussed in the limited enthusiasm model.

Why Do People Leave the Church?

People leave the church for many reasons. Some renounce the faith and return to the world. Some still claim to be Christian but no longer attend church. This model does not make any spiritual judgment on those that leave church, in the same way as it makes no assumptions of those who belong. It merely divides leavers into those who become open to rejoining and those who do not, reversion.

Reasons for people leaving church include:

  • Physical persecution. At its most extreme believer's lives could be in danger, as frequently happened in the early church. Christians would be asked to swear allegiance to Caesar and curse Christ, or face death. Those who succumbed were no longer welcomed in the church. The fear of this test caused many others to renounce the faith also.
  • Psychological persecution. Some believers give up the faith due to pressure of unconverted family or peers. The pressure may take the form of teasing or being shunned from normal social activities. The believer gives up the church to have an easier life.
  • Some of the believers were not truly converted in the first place and give up the faith once it loses its initial attraction. The unbelieving world they left behind has proved more attractive to them.
  • The believer may have fallen into sin and caused them to be to ashamed to be part of the church anymore.
  • The believer may have been hurt by others in the church. It is now too painful for them to be part of the church with those who hurt them. Sometimes it is to painful to be in any church as it reminds them of the past hurt.

How Do the Children of Believers Become Part of the Church?

Children are not normally born with a faith. However if a child is brought up in the Christian faith it is the hope of Christian parents that they will believe for themselves and join the church. This is often called biological growth to distinguish it from conversion growth. Of course the children at some point should become converted! However their conversion has taken place within the Christian community rather than from the world outside. In this model such children will be regarded as being "born as believers".

There is a time lag between birth and the formal adoption of such children into the church. This time lag will vary according to church policy - anything from aged 6 to 18! It will also vary depending on whether the model is compared with attendance, membership or communicant figures. In this model this time lag is ignored.

Why Do the Children of Believers Fail to Become Part of the Church?

  • Some are not converted and thus see no reason for belonging to the church. Although familiar with the church's culture spiritually it is meaningless to them.
  • Some churches offer so little that even converted children see little point in joining. However the absence of Christian friends does not enable them to easily join another church which is a huge step for a young person.
  • Young people are very sensitive to hypocrisy. Both perceived and actual hypocrisy in the adult generation will cause young Christians to prefer to be believers "who do not attend church".

Why Do Unbelievers Harden or Soften?

An unbeliever may be hardened because they have had a bad experience of the church; either as a former member, or through contact with church members. Any message they hear from church may only reinforce their negative views rather than lead to conversion or them trying a church out. They may harden through negative media coverage of church or through the views of other unbelievers they meet. However over time such hardened attitudes may soften, either through age, the fading memory of what caused them to be hardened, or through a different experience of church.

Hardened unbelievers may include people in rival religions, denominations, or those for whom Christianity is a culture they do not understand. Time is needed to bridge these gaps. The model does not include details of why hardening or softening occur, only that they occur at fixed rates. The rates can be set to model the effects of secularisation, or the effects of a society becoming more accommodating of Christianity.

Children of open unbelievers may become hardened, perhaps due to increasing cultural distance of a new generation. Children of hardened unbelievers may become open, perhaps due to not acquiring their parents cultural baggage.

Model Parameters

The behaviour of the model is controlled by a number of parameters that reflect the church's effectiveness, and the response of society:


Reproduction Potential This is the number of unbelievers converted, and made enthusiasts, through one existing enthusiast, given the whole population are unbelievers. It measures how much an enthusiast can "reproduce" themselves from of the pool of unbelievers.
Duration of Enthusiastic Phase The average length of time and enthusiast is active in conversion, before they become an inactive believer.
Fraction of Converts Enthusiast The fraction of new converts who become enthusiasts. The remainder become inactive believers immediately on conversion.
Leaving Rate The total rate at which people leave church regardless of whether it is reversion or leaving to the open category.
Fraction of Believer's Children Retained in Church A fraction each for inactive believers and enthusiasts who leave church before adulthood. Also the fractions of those who leave who become open or hardened unbelievers.
Fraction of Unbeliever's Children Who are Either Hard or Open A fraction of children of hardened unbelievers may be open, and a fraction of children of open parents may be closed.
Hardening Rate The fraction of the open unbelievers who become hardened per year.
Softening Rate The fraction of the hardened unbelievers who become open per year.
Birth and Death Rates Church and outside society can have separate birth and death rates, to model aging and religions with higher average family size.
Initial Fraction of Church Enthusiast The fraction of the church that are enthusiasts at the start of the model.
Initial Fraction of Unbelievers Hardened The fraction of unbelievers that are hardened at the start of the model.

Results of the Limited Enthusiasm with Demographics Model

There are implications for the long-term growth and decline of the church. Like the basic limited enthusiasm model there is a revival growth threshold over which the church will see rapid growth. However there is also an extinction threshold under which the church will decline to zero members or attenders.

See Long-Term Growth Results.

See Long-Term Decline Results.

Home | Models | Results | Simulations | Articles | Revival | References | Publications | Modelling | Blog | About | What's New | Contact

Church Growth Modelling