Limited Enthusiasm with Migration
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, where its value is determined by outside factors.
The model predicts a threshold of revival-growth which depends on the size of the community that remains unconverted. 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
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 is not modelled but could be due to:
- A town or a suburb is expanding due to house building.
- People become more mobile and are willing to travel further to church.
- Churches close and there is less local competition.
- The church plants a mission church in a nearby community.
- For a national church denomination it could be people migrating into the country.
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
Each category can be enhanced by migration. Because migration is determined by outside factors, neither church nor society have control over its value thus no new feedback loops are added.
The behaviour of the model is controlled by a number of parameters that reflect the church's effectiveness, and the response of society:
||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.
||Separate rates for unbelievers, enthusiasts and inactive believers
|Initial Fraction of Church Enthusiast
||The fraction of the church that are enthusiasts at the start of the model.
||Birth 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 exhibits 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 it is possible for a church to have repeated revivals due to the continued expansion of the susceptible pool of unbelievers tipping the church back over the revival threshold.