John Hayward

A General Model of Church Growth and Decline

ABSTRACT An earlier model of church growth (Hayward, 1999) is extended to include long-term effects due to births, deaths and reversion from the church. It is proposed that only a subset of the church, the enthusiasts, is involved in the recruitment process, and only for a limited period of time after their conversion. It is found that the church reaches equilibrium in its proportion of society according to the potential of these enthusiasts to reproduce themselves, and the losses from the church. If this reproduction potential is below a threshold that depends on losses, then extinction occurs. If it is above a higher threshold, then the church sees rapid revival growth. The model is applied to a number of church denominations to examine their prospects for survival or revial growth. Generally, declining churches do so because their reproduction potential is inadequate, rather than due to excessive losses.

Mathematical modeling of church growth

The possibility of using mathematics to model church growth is investigated using ideas from population modeling. It is proposed that a major mechanism of growth is through contact between religious enthusiasts and unbelievers, where the enthusiasts are only enthusiastic for a limited period. After that period they remain church members but less effective in recruitment. This leads to the general epidemic model which is applied to a variety of church growth situations. Results show that even a simple model like this can help understand the way in which churches grow, particularly in times of religious revival.

The Future of Bilingualism: An Application of the Baggs and Freedman Model

The original paper (Baggs and Freedman, 1990) gave a model of the interaction of a bilingual with a unilingual population. This paper examines the original in an exhaustive fashion and identifies four possible scenarios in the long-term future of the bilingual population. Equilibrium points are found in a manner conducive to practical interpretation, and their stability is investigated. The original model is then applied to the situation in modern Wales and more briefly to that in Scotland, Ireland and Brittany. In conclusion the capacity of the model to inform policy is considered, and an amended model is suggested.

Activist model of political party growth

The membership of British political parties has a direct influence on their political effectiveness. This paper applies the mathematics of epidemiology to the analysis of the growth and decline of such memberships. The party members are divided into activists and inactive members, where all activists influence the quality of party recruitment, but only a subset of activists recruit and thus govern numerical growth. The activists recruit for only a limited period, which acts as a restriction on further party growth. This Limited Activist model is applied to post-war and recent memberships of the Labour, Scottish National and Conservative parties. The model reproduces data trends, and relates realistically to historical narratives. It is concluded that the political parties analysed are not in danger of extinction but experience repeated periods of growth and decline in membership, albeit at lower numbers than in the past.

OR and language planning: modelling the interaction between unilingual and bilingual populations

OR methodology is applied to the contemporary concern of modelling language group interaction, with a view to language planning. The change in size of two unilingual language groups, and of a third bilingual population mediating the interaction of these, is modelled using system dynamics. The model is one of highest possible endogeneity, with the minimum of external intervention in modelling runs. The model is applied to the instances of modern Canada excluding Quebec, Quebec, all Canada and Wales, and conclusions drawn regarding the use of the model in determining language planning initiatives.

A Model of Language-Group Interaction and Evolution Including Language Acquisition Planning

A model of language-group interaction as modified by deliberate language acquisition planning (LAP) is given. The behavior of the model while LAP measures are in force (First Regime or Regime 1) is distinguished from the longer term when natural interaction is re-established (Second Regime or Regime 2). Both regimes are subclassified into scenarios according to inherent long-term behavior, and an attempt is made to classify real-world examples of LAP and natural interaction in terms of these. Conclusions are drawn regarding the assumptions of LAP, and the use of the model in the allocation of resources to LAP initiatives.

Refinement of Z specifications using reusable software components in Ada

A method of refining 2 specifications into Ada using reusable software components is presented. Software oomponents are written to model the data structures supported by Z, such as sets and functions, enabling the data model of the abstract specification to be implemented directly. The operations of the specification are then implemented from their predicates using the operations of the Z software components. The method is illustrated using a simple specification.