Several years ago, I wrote a post that showed how to calibrate Stella and iThink® models using PEST, a third-party calibration tool (Using PEST to Calibrate Models). Starting with version 1.5, Stella Professional and Stella Architect have optimization built in. Since calibration is a special case of optimization, we can also use this feature to calibrate models (but stay tuned: calibration will be added as its own feature in the not too distant future). Let’s review the problem that was calibrated using PEST in that post and then configure the optimization to calibrate it within Stella.
The model is a simple SIR model first presented in my blog post Limits to Growth and shown below (this version with all the optimization settings can be downloaded here). There are two parameters: infection rate and recovery rate. The Population size and the initial number of Infected people are also model parameters, but do not need to be calibrated (presumably, we know the population and the data tells us the initial number of infected people).
The Data Set
We will calibrate this model to the data set of the number of weekly deaths caused by the Hong Kong flu in New York City over the winter of 1968-1969 (below).
Here, I am using the number of deaths as a proxy for the number of people infected, which we do not know. This is reasonable because the number of deaths is directly proportional to the number of infected individuals. For this specific outbreak, less than 0.5% of infected people died, so we could multiply these numbers by 200 (1/0.005) to approximate the number of people infected. As I did not do this for the PEST calibration and wish to compare the results, I will not do this here either.