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 renewal model extends this model to allow for existing inactive believers to be “renewed” in the faith and also become 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 and infecting inactive believers, enabling them to be agents in conversion.

The following model details supplement the Renewal Model Overview.


The model consists of three groups of people: unbelievers, enthusiasts (or active believers) who alone are responsible for spreading the faith, and inactive believers. If demographic effects are included, unbelievers are split into those who are open to conversion and those who are hardened against it.

The renewal model is built on the Limited Enthusiasm model and the Demographics extension, where the assumptions are explained further.

Dynamic Hypotheses

The dynamic hypotheses are:

Conversion Through EnthusiastsEnthusiasts are responsible for 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 numerous means.
Loss of EnthusiasmAfter a period of time, enthusiasts lose their potential to convert. This slows and limits growth.
Diminishing Susceptible PoolAs 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 EnthusiastsNot every convert becomes an enthusiast. Some become immediately inactive.
Renewal of Inactive BelieversEnthusiasts are responsible for making inactive believers enthusiasts through contacts within the church. The more believers they renew, the more enthusiasts made. This accelerates the production of enthusiasts and enhances conversion growth. Renewal can be done through many means.
DemographicsThere are many assumptions connected with births, deaths, leaving the church, reversion, softening and hardening of unbelievers, as in the Demographics model.

System Dynamics Model

The above hypotheses are expressed in a system dynamics model, with the central ones indicated in figure 1:

Renewal Model stock and flow diagram
Figure 1: Limited Enthusiasm Model with Renewal


The equations of the renewal model are:

renewal model equations

where the potential number of believers renewed is given by.

When the church C is small, transmission is governed by “mass action” where people’s contact networks are small. As the church gets larger, the transmission becomes standard incidence as the contact network is too large for everyone to be reached. Other parameters are given below.

What is Meant by “Spreading the Faith”?

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

How Do Believers Get Renewed?

  1. The believer sees a spiritual life in other Christians far more appealing than their own. Their dissatisfaction with their spiritual state leads them to seek Jesus Christ and ask for a similar quality of life. That quality of life becomes noticeable to others.
  2. The believer comes into contact with organisations that promote a more vibrant form of Christianity: “deeper life”, “spirit-filled”, etc., or courses such as the Alpha or Christianity Explored. Perhaps they are taken by friends to conventions such as Spring Harvest or New Wine. The subsequent life changes impact their unbelieving friends. Even just identifying with such organisations has an influence.
  3. Some of the “believers” were not truly converted in the first place. Although they belong to the church, they may have joined for social reasons rather than spiritual ones. Their contact with enthusiasts within their church has become the means of their conversion.
  4. The “renewal” may manifest itself as a burden for the state of the lost impressed on them by some other Christian, launching the believer into evangelistic activity. This may come through participation in evangelistic training courses or discipleship classes.


All demographic aspects are discussed in the demographics model.

Model Parameters

The behaviour of the model is controlled by several 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 the pool of unbelievers.
Renewal Potential
This is the number of inactive believers made enthusiasts, through one existing enthusiast, given the whole church are inactive. It measures how much an enthusiast can “reproduce” themselves from within the church.
Duration of Enthusiastic Phase
The average length of time an enthusiast is active in conversion before they become an inactive believer.
Fraction of Converts Enthusiast
The fraction of new converts who become enthusiasts. The remaining people become inactive believers immediately on conversion.
Initial Fraction of Church EnthusiastThe fraction of the church who are enthusiasts at the start of the model.
Demographic ParametersBirth and death parameters, leaving and reversion rates, hardening and softening rates. See Demographics model.

Model Results

Model Results