The central hypothesis of the constant demand model is that a church does no work to recruit members but relies on a constant demand in society, a fixed number of people coming to church each year. Although there is demand for religion, the church puts no effort into supplying the demand, or into creating it.

In addition, losses to the church, whether through deaths or people leaving, are at a constant rate per person.

The model predicts a limit to the growth of the church, with growth slowing as the limit is reached.

This is a metaphorical model whose purpose is to illustrate limits to church growth.

System Dynamics Model

Unbelievers are added to the church at a constant rate. Church members leave at a constant rate per person. Thus people stay in church for a constant average length of time, loop B, figure 1.

Constant demand stock-flow model
Figure 1


Without loop B, the church would increase steadily through the constant demand, the flow “come to church”. With B, the feedback: more church, more leave, thus less church, gives exponential deceleration. Thus growth halts when the number of people leaving rises to match the demand, figure 2.

Constant Demand Results
Figure 2

For further results see Constant Demand Results.


The model consists of one group of people: “Church”, either a single congregation, or a local group of congregations, or a denomination. “Church” may be measured by attendance or membership.

The dynamic hypotheses are:

Constant demand from society for church/religion.No effort is made by church members to contact people in society to bring them to church. Thus the size of the church has no effect on the number who come to church. The constant demand for the church in society may be due to the church’s fixed actions, such as advertising. It may also reflect a constant demand for the type of religion offered by the church.
People leave church at a constant proportional rate (B).
This process includes people giving up the church and deaths. The reasons why they leave are personal; thus, the rate is proportional to the church size, i.e. “per capita”.
Unlimited pool of unbelievers.The size of society outside the church is infinite and provides no limit to church growth.

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:

come to churchThis is the number of unbelievers who join the church each year. This parameter represents society’s demand for the religion of the church
percentage leaving rateThe fraction of church members who leave each year.

Further Results.