Stella 9.1 model can be downloaded from http://forio.com/simulate/jhayward/lbdr-anglican-79-98/model/download/?hard=true.
Model author: John Hayward, Church Growth Modelling.
Demographics Model Simulation
Church of England 1979-1998
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. The demographics model adds births, deaths, reversion and secularisation.
This model is the simulation in "A General Model of Church Growth and Decline", Journal of Mathematical Sociology, Hayward, 2005. It was achieved by optimising four parameters next to survey data from Christian Research, 1979, 1989, 1998. The four parameters are the reproduction potential, the duration enthusiastic, the reversion rates (set equal) and the initial fraction of the church enthusiast. The optimised parameter values appear in the first line of table 1 in the paper.
At that point the Church of England was well under the extinction threshold. By 2009 the estimates had changed to it just avoiding extinction. Data to 2012 suggests that optimism has not been maintained.
Opens in separate window: http://forio.com/simulate/jhayward/lbdr-anglican-79-98.