In the variable demand model, the conversion rate is proportional to the number of people open to conversion. The limit to church growth caused by constant demand can be removed by making the demand proportional to the number of people who might join the church. That is, there is a constant per capita demand, a fixed percentage joining each year. Thus, the more open believers, the more join the church, a balancing loop B1, figure 1:

Figure 1

With this single process, every open believer eventually joins the church. However, the purpose of this model is to show that even with the growth limit caused by demand lifted, the church’s growth is limited by people leaving the church.

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

System Dynamics Model

In addition to the process B1 in figure 1, people leave the church at a constant per capita rate, B2, figure 2. Church leavers are temporarily hardened and not open to re-conversion. Hardened unbelievers become open at a fixed per capita rate B3. The full system dynamics model is in figure 2:

Stock flow diagram of the variable demand model
Figure 2


In this model, the church always survives and can never become extinct. The three population groups stabilise at values determined by the three removal rates, figure 3. Clearly, key processes are missing. It is a good exercise to work out what needs to be added that so that a church could potentially go extinct.

Graph of church numbers in the variable demand model
Figure 3

The leaving rate of the church puts a limit on the growth of the church despite a healthy joining rate.

See further results of the variable demand model.


The model has three stocks: church members, hardened unbelievers and open unbelievers. Their total is constant.

Unbelieving society demands church/religion at a rate proportional to its size (B1).Each person in society has a demand for religion, set at the average value. Thus, the demand in society is proportional to the number outside the church. As people join the church, then demand falls. Therefore, there is no effort by the church to increase demand.
People leave church at a constant proportional rate (B2).This process includes people giving up the church and deaths. The reasons people leave are personal; thus, the rate is proportional to the church size, i.e. “per capita”. Those who leave are open to rejoining. Those who die are matched by births.
Hardened Unbelievers become open unbelievers at a constant rate (B3).This process assumes a constant average length of time that unbelievers are hardened. I
Limited pool of unbelievers.The size of society outside the church is finite.


The behaviour of the model is controlled by three parameters that reflect the joining, leaving and the transition from hardened unbelievers to open.

joining rateThe fraction of open unbelievers who join the church each year. This parameter represents society’s demand for the religion of the church.
leaving rateThe fraction of church members who leave each year.
softening rateThe fraction of hardened who become open each year

Further Results