MathBench > Population Dynamics

Stage-based Models

A really simple model

The first line of the scroll gives the initial conditions of the model – in other words, what the population looked like in the initial or early stages. The second line gives the current status of the population. The third line is the beginning of a very simple model (much too simple, but we’ll use it to demonstrate how to go about setting up a better model).

The model we are building uses rates of change. In other words, if I know how many people are in each compartment today, and I know how many people are moving (or changing compartments), then I know how many people will be in each compartment tomorrow. This process is called iterating the model.

So the equation

It = It-1 + 2

says that in order to find todays number of sickies, I take yesterday’s number and add two. Or in simpler language, every day 2 more people get sick. But where is the rate of change in this equation, you may ask. That is a good question. In fact you need to rearrange the equation slightly to see it as a rate of change:

It - It-1 = 2, or

Delta I = 2

Since the delta notation is more compact, we’ll use it from now on.