A small ODE model of how service quality shapes customer retention. Every customer sits in one of three buckets — Good, Neutral, or Bad opinion of the business — and moves between buckets based on the quality of service they receive and the word-of-mouth it generates. Bad experiences travel faster than good ones: the model assumes one satisfied customer tells one person, while one unhappy customer tells three.
The chart below is a live, in-browser re-solve of the original MATLAB ode15s system (reproduced faithfully in JavaScript), starting from 1,000 neutral customers and no service history.
Simulated with Good = 45%, Neutral = 40%, Bad = 15% service quality mix and a service rate of 20 customers/day — the same parameters as the source model. Hover the chart for values at a given day.