A deterministic model for church growth with internal revival

Churches have played an important role in the development and shaping of societies in the world. An extension of a previously proposed theory for church growth is presented and analyzed using a mathematical modelling approach. The extension presented incorporates exposure before conversion and internal revival that results in the restoration of enthusiasm. The results are presented in terms of R₀, the church reproduction potential. The incorporation of a class of the exposed and internal revival allowed the existence of a subcritical (backward) bifurcation at the critical value R₀ = 1 and hence the existence of multiple equilibria for R₀ < 1. The results suggest that having R₀ < 1 does not necessarily lead to a decline in church growth leading to extinction. Numerical results show that when internal revival is taken into account, R₀ does not accurately describe the invasion strength of the church.