Results of the Spiritual Life Through Activists Model

According to the Bible, there are times when the Holy Spirit descends upon the church. This type of event is called a Baptism with the Holy Spirit, a baptism carried out by the Lord Jesus himself. The baptism is related to revival when one or more individuals, usually believers, are transformed in their confidence in God’s presence and are empowered by Him to witness. Often, many conversions follow, and other believers are baptised with the Spirit..

My question here, is how can the effects of this baptism with the Holy Spirit be model? Clearly, the effects in a person’s soul cannot be modelled. That is outside the scope of the model! Also, we can’t place the baptism in a feedback loop. By definition, the baptism is exogenous, it is work of God.

Modelling the Effect of a Baptism with the Holy Spirit

However, the Spiritual Life Model can capture the effects of the baptism on church dynamics by allowing the variable Spiritual Life to have a sudden increase. Figure 1 shows the Spiritual Life submodel. The effect of the Holy Spirit’s work is represented by an addition to the inflow increase in SL. The effect is controlled by the amount of the baptism, that is, how much it influences the church’s spiritual life. The duration of the baptism, that is, how long the effect of spiritual life persists, is a further control parameter.

Figure 1: Spiritual Life Submodel with the Effects of a Baptism with the Holy Spirit

Church Numbers and Spiritual Life

I will start the model in equilibrium with church numbers at 22% of the total population. The outpouring of the Spirit occurs at 50 years after the start of the run and continues for 25 years. At 50 years, there is a sharp rise in the church’s spiritual life. However, it is not sudden. A step rise in an inflow causes a delayed rise in its stock due to accumulation over time. The increase in church numbers is smoother and further delayed as it takes time for the enlivened enthusiasts to impact the population and produce converts.

Figure 2: Spiritual Life and Church Numbers after a Baptism with the Holy Spirit

The increase in spiritual life due to the baptism is switched off at 75 years. However, the value of spiritual life in the church takes time to fall, Figure 2. Spiritual life tends to fade when averaged over many people, rather than end suddenly. The peak in church numbers occurs after the revival baptism has finished. Indeed, spiritual life has almost returned to its pre-baptism level. If revival is measured by church growth and conversions, people may think the revival is still continuing. It would be more correct to say that the effects of the revival continue past the end of the spiritual work. If revival is measured by the work in the souls of believers (assuming that were possible), then it does indeed end at 75 years.

Oscillations

What may be of concern is that the church numbers fall below the equilibrium, e.g. at 150 years, and oscillate for many years. Why does this overshoot happen? The answer lies in the Limited Enthusiasm Model’s structure. In that model, I assumed that enthusiasts are generated solely from new converts. There is no renewal process that could generate them from activists or even inactive believers. Thus, new converts cannot be generated until the unbeliever numbers have risen through people moving along the system.

Enthusiasts and Activists

Figure 3 shows the church’s constituent population numbers. The enthusiasts rise first, then the activists (the next group in the chain), then the inactive. Further, I have used a simplified model where people only leave the church from unbelievers, rather than enthusiasts and active, as in the full demographic model. This omission accentuates overshoot and oscillations. Thus, in real life, they would be less pronounced. If renewal had been included, the overshoot would almost disappear.

Figure 3: Church Populations after a Baptism with the Holy Spirit

Reproduction Potential

Figure 4 illustrates the effect of the Baptism with the Holy Spirit on the reproduction potential, mirroring the pattern in Spiritual Life, Figure 2. The potential immediately exceeds the revival threshold, leading to conversions. However, conversions only increase slowly, giving a gradual rise in church numbers, Figure 2. As the church grows, the revival threshold grows, Figure 4, as the pool of available unbelievers shrinks. By 75 years, the threshold exceeds the reproduction potential, made more dramatic as the reproduction potential drops after the end of the effects of the baptism. Due to oscillations, there is a further small period of revival growth after year 125.

Figure 4: Reproduction Potential, Revival Threshold and Baptism with the Holy Spirit

Further Results of the Spiritual Life Model