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. The model is extended to include migration of people into the catchment area of the church. Its value is determined by outside factors.

The model predicts a threshold of revival-growth that depends on the size of the unconverted community. If the potential for enthusiasts to reproduce themselves is over that threshold, then rapid growth results. With migration, it is possible for repeated revival-growth to occur as the pool of unbelievers is continually replenished.


The model consists of at least three groups of people: unbelievers, enthusiasts who alone are responsible for spreading the faith, and inactive believers. If demographic effects are included then unbelievers are split into those open to conversion and those hardened against. See Limited Enthusiasm and Demographics for full details of the core model and dynamic hypotheses.

The additional dynamic hypothesis of the migration model assumes constant migration, with independent rates into enthusiasts, inactive believers and unbelievers. The details of why migration occurs are not modelled but could be due to:

  1. A town or a suburb is expanding due to house building.
  2. People become more mobile and are willing to travel further to church.
  3. Churches close and there is less local competition.
  4. The church plants a mission church in a nearby community.
  5. For a national church denomination, it could be people migrating into the country.

System Dynamics Model

Unbelievers convert to believers through contact with enthusiasts who have “spread the faith” to them, figure 1. 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.

Figure 1

Each category can be enhanced by migration. Because migration is determined by outside factors, neither church nor society has control over its value; thus, no new feedback loops are added.

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 PotentialThis 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 the pool of unbelievers.
Duration of Enthusiastic PhaseThe average length of time and enthusiast is active in conversion before they become an inactive believer.
Fraction of Converts EnthusiastThe fraction of new converts who become enthusiasts. The remainder becomes inactive believers immediately on conversion.
Migration RatesSeparate rates for unbelievers, enthusiasts and inactive believers
Initial Fraction of Church EnthusiastThe fraction of the church that are enthusiasts at the start of the model.
Demographic ParametersBirth and death parameters, more general leaving and reversion rates, hardening and softening rates. See Demographics model.

Results of the Limited Enthusiasm Model with Migration

The solutions exhibit the typical steep rise in the growth of the church, eventually slowing down well short of the whole community being converted. Such growth only occurs if the reproduction potential exceeds a threshold of revival-type growth which depends on the proportion of unbelievers in society only.

With migration, a church can have repeated revivals due to the continued expansion of the susceptible pool of unbelievers tipping the church back over the revival threshold.

See Migration Results.