MathBench > Population Dynamics

Stage-based Models

Iterating the Simple Model

So here is our first, most basic model:

Initial conditions:

On day 1: S: 599 I: 1 R: 0

Rates of Change:

Delta I = 2

Timestep = 1 day

If you iterated this model for one year, what would the graph of number of infected people look like?

(applet – draw on graph and click for correct answer)

Probably you have noticed a couple of problems with this very simple model. For one thing, we have 3 compartments in the model, but we only specified a rate of change for one of them.

So, let’s fix that problem right away. First of all, let’s assume we have a fixed total population size. That is, we assume that no one is going to die, that no one is going to be born, no new students will enter during the year, and no one gets expelled or drops out. These are simplifying assumptions but they are not too unrealistic (well, unless there’s a major battle with Valdemort or something).

So if the population size is fixed, then whoever goes into one compartment has to come out of some other compartment. For example, if 2 kids enter the infected compartment, there must be 2 less kids in the susceptible compartment (remember, once you recover from the disease, you’re forever immune, so the newly sick kids can’t come from the recovered group). Fill in the equations below:

(applet Delta S = Delta I = Delta R = 0 Check graph)