Activists are believers who contribute to the life of the church. They are a more general group than enthusiasts whose specific role is to make converts. There will be many other active people in the church who are not involved in conversion. The Limited Enthusiasm Model is extended to include active believers. This extended model will be useful in sociological models of church growth dealing with such issues as spiritual life and institutionalism.

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. New converts become new enthusiasts. 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. There are also activists in the church who, though not active in recruitment, are active in other areas of church life.

Church growth is limited as enthusiasts fail to reproduce themselves from a shrinking pool of potential converts. The church will consist of a balance of enthusiasts, other activists and inactive believers.

System Dynamics Model

Stocks and Flows

This model has three types of Christians:

  • Enthusiasts – those active in conversion;
  • Active Believers (Activists) – those active in the church but not in conversion. They are “non-recruiting” activists.
  • Inactive believers – who play no part in conversion or any other aspect of church life.

These three types of church people are represented by three stocks in figure 1. Enthusiasts will also be active in other aspects of church life. Thus, the total activists are the sum of enthusiasts and active believers. The other stock represents the number of unbelievers.

Limited Enthusiasm with Activists - SD Model
Figure 1: Limited Enthusiasm Model with Activists


Unbelievers convert to believers through contact with enthusiasts who have “spread the faith” to them, loops R and B1. Some new converts become enthusiasts, some become activists who do not recruit, and the remaining converts become inactive believers. Enthusiasts only remain active for a limited time before becoming inactive and taking no further part in spreading the faith, loop B2. However, they remain active in other aspects of church life.

Active believers only remain active for a limited time before they become inactive, loop B3. This time is likely to be much longer than the duration enthusiastic as many active Christians are active for most of their lives.

In this simplified model, only inactive believers leave the church, loop B4. After becoming unbelievers, they are open to re-conversion driving future growth, loop R2. The delays in the process can cause long-term oscillations in church numbers.

The model may be enhanced with births, deaths, hardened unbelievers and reversion from all categories. See the Demographics model. The enhanced model enables more accurate calibrations, though the general model behaviour is the same.


The system dynamics model reduces to four differential equations:

Limited Enthusiasm with Activists - Differential Equations


The model has eight parameters.

Reproduction Potential RpThis is the number of unbelievers converted and made enthusiasts, through one existing enthusiast, given the whole population are unbelievers. It measures how much enthusiasts can “reproduce” themselves from the pool of unbelievers.
Duration of Enthusiastic Phase τiThe average time an enthusiast is active in conversion before they become an activist who does not recruit.
Duration of Active Phase τaThe average time spent as an activist is active before becoming inactive.
Fraction of Converts Enthusiast gThe fraction of new converts who become enthusiasts. The remaining people become either active or inactive believers immediately after conversion.
Fraction of Converts active fThe fraction of new converts who become activists. The remaining people become inactive believers immediately after conversion.
Leaving Rate αThe total rate at which inactive believers leave the church.
Initial Fraction of Church EnthusiastThe fraction of the church that are enthusiasts at the start of the model.
Initial Fraction of Church ActivistThe fraction of the church that are activists at the start of the 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, figure 2. However, there is also an extinction threshold, equal to unity, under which the church will decline to zero members or attenders.

Figure 2

The peak in the total church is later than that of the total activists (including enthusiasts), figure 3. This delay will have significance when sociological variables are included. Those driven by the whole church, or by inactive believers, will take longer to respond than those driven by the church activsits.

Figure 3

Further Results


The concept of activists comes from modelling the growth of political parties. See:

  • Jeffs R.A., Hayward J., Roach P.A. & Wyburn J. (2016). Activist Model of Political Party Growth. Physica A: Statistical Mechanics and its Applications, 442, 359-372. arXiv:1509.07805. Physica A.
  • Hayward J., Jeffs R.A. & Roach P.A. (2020). A Supply and Demand Model of Political Party Growth. Presented at the 36th International Conference of the System Dynamics Society, Virtual Bergen, July 2020.