Limited Enthusiasm Models
Enthusiasts are the subset of the church who are active in the conversion of unbelievers. They are “infected” with religion and pass it on to their friends, family and contacts. The result is that religion spreads like a disease, and the church grows. Growth ceases because enthusiasts lose their infectious enthusiasm and are thus unable to convert people fast enough from the shrinking pool of unbelievers. These hypotheses can be expressed in the system dynamics diagram of the limited enthusiasm model:

There are three categories of people: unbelievers, enthusiasts (or active believers) and inactive believers. These correspond to the susceptible, infected and removed categories in the spread of an infectious disease.
In the basic model, new converts are the primary source of enthusiasts because they have the most contact with unbelievers. Extended models include births as a source of believers (Demographics Model), existing believers as a source of enthusiasts (Renewal Model), and the work of the Holy Spirit in conversion (Spiritual Life Model).
The Models
Limited Enthusiasm – Revival
Understanding the dynamics of revival by analogy with the spread of disease. Revival growth threshold – how a small number of enthusiasts can make a big difference.
Demographics
Long-term Limited Enthusiasm model, including births, deaths and leavers. Extinction threshold and the survival of churches and denominations.
A version with only reversion is sometimes used for short-term data fitting.

Activists
The church can be divided into three types of believers: enthusiasts – who recruit, activists – who do other work in the church, and inactive believers. Although active believers may not contribute directly to the growth of the church, they may do so indirectly by building up the church’s spiritual life and spiritual capital.

Renewal
Growing the church by spiritually renewing its members. Enthusiasts are generated from existing inactive believers. Such renewal allows a critical mass of enthusiasts to initiate revival.

Spiritual Life
Enthusiasts generate spiritual life in the church, which in turn makes them more effective in conversion. Spiritual life covers works that build people up in Christ through the Holy Spirit and glorify God.

Membership
Membership figures are generally greater than attendance figures in declining churches. Vice versa in growing churches. How does this come about?
Migration
Inward migration can be a big help in growing a church. It can even tip a church into revival growth.