Week 2: The Pain Equation

After the first week of familiarizing myself with the Numerus interface, the time had come to begin work on the dynamic model of pain. In order to start this incredible undertaking, Professor Darling and I decided on a top down approach to constructing the model. The current understanding of pain is that it is a function of other factors, which themselves may be functions of other factors. At a base level, an equation for pain was required before we could proceed any further.

eq
The General Form of the Logistic Growth Equation

In keeping with the logic of pain, a logistic growth equation was utilized. Using logistic growth equations in statistical modeling has been commonplace in environmental science for decades, and we believed that the principles held over when thinking about pain. In the original environmental context, population growth was modeled over time by multiplying the current population times a growth rate r. In order to impose a limit on the growth, rP was multiplied by (1 – P/K), where K is the carrying capacity, the largest size the population can grow to.

When conceptualizing the equation in terms of pain, I was guided by 2 principles which Prof Darling echoed several times over the course of the project.

  1. Pain can never be negative
  2. If you do nothing about your pain, it will get worse

Therefore, I set up the equation rpain * Pain * (1-Pain/Kpain), where pain level changes as a result of the growth rate of pain times the current pain level, and is limited by the carrying capacity. While this equation did provide the graph I was looking for, I soon discovered that modeling pain is not quite that simple.

graph1
The Graph Produced by the Logistic Pain Equation

 

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