##### Application of the Limited Enthusiasm Model

Rapid growth in the churches in Wales occurred during 1904-5 in what is sometimes known as the “Evan Roberts” revival or even the Welsh Revival. Wales has had many revivals but this has become the most famous. In 1904 the combined total membership for Welsh churches stood at 48.94% of the total population and rose to about 56% by the end of 1905. The bulk of the 100,000 converts came in about 12 months (see Hayward 1999).

Simulations show that the reproduction potential for each active believer (enthusiast) was just over 2. If all converts had also become enthusiasts, then the potential number converted by each enthusiast was also 2 with the duration of the enthusiastic phase about 1 week. The actual number converted was thus 1 per enthusiast, half the value of the potential number. This is because about 50% of the people a typical enthusiast met were already converted. One enthusiast only needed to bring one other person to a meeting where they also became converted and an enthusiast!

Figure 1 shows the results of a system dynamics model of this Welsh Revival, calibrated to data, starting in November 1904. The data points at months 2, 3 and 4 are computed using conversion data from newspaper reports of the Welsh Revival (Western Mail). The final figure in month 13 is determined from the end of the year membership figures for all churches in Wales, confirming the 100,000 converts widely reported at the time.

The percentages of church members and unbelievers are shown in figure 2. The percentage is computed by comparing numbers with the total adult population of Wales in 1904.

It is not possible to tell how many of the converts also became enthusiasts. If it was only 10% then the conversion potential would have to be much higher, around 18 converts per enthusiast, and the enthusiastic phase longer, about 1 month (see Hayward 2000).

In reality, these parameters could vary widely for different enthusiasts, with the model yielding their average values.

Further details of the calculations are given in the explanatory notes, including a breakdown of the figures associated with each denomination over the period.