Introduction to Dynamic Models

Abstract

The concept of a differential equation as a model is introduced here as a buffer that modulates sharp changes in an input signal by spreading out the change on the output side. Six examples are taken up, which will reappear later in the book. Each of these examples involve data spread out over the interval of change that will be used later to estimate parameters defining the differential equation. The introduction of vaccination for smallpox in Montreal in the 1870’s and the subsequent decline in deaths, followed by the re-introduction of the disease in 1885 and the subsequent epidemic open the story. The final example models the production of a complex handwriting of “statistics” in Mandarin, and demonstrates that a simple step function input, when passed through a spring-like buffer, can closely capture the curves, cusps and lifts in the actual script. The chapter closes with an overview, an outline of the mathematical skill level required to read the book, and the goals motivating the rest of the book.