Database Reference
In-Depth Information
DT to reflect ever-smaller periods until the change in the critical variable is within
measuring tolerances. The best guide in the determination of the proper modeling
time step (DT) is the “half rule.” Run the model with what appears to be an ap-
propriate time step, then halve the DT and run the model again, comparing the two
results of important model variables. If these results are judged to be sufficiently
close, the first DT is adequate. One might try to increase the DT if possible to make
the same comparison. The general idea is to set the DT to be significantly smaller
than the fastest time constant in the model, but it is often difficult to determine this
constant. There are exceptions. Sometimes the DT is fixed at 1 as the phenomena
being modeled occur on a periodic basis and data are limited to this time step. For
example, certain insects may be born and counted on a given day each year. The DT
is then 1 year and should not be reduced. The phenomenon is not continuous.
You may also change the numerical technique used to solve the model equa-
tions. Euler's method is chosen as a default. Two other methods, Runge-Kutta-2
and Runge-Kutta-4, are available to update state variables in different ways. These
methods will be discussed later.
Start with a simple model and keep it simple, especially at first. Whenever pos-
sible, compare your results against measured values. Complicate your model only
when your results do not predict the available experimental data with sufficient ac-
curacy or when your model does not yet include all the features of the real system
that you wish to capture. For example, we realize that the SICK do not remain so
forever. Assume that they are sick for 25 days (SICK TIME) and then they get well.
What is the new steady state level of SICK under these circumstances? To find the
answer to this question, define an outflow from the stock SICK and name it GET-
TING WELL, the number of SICK who recover per day. There are at least two ways
to evaluate this part of the model. We could just add the outflow GETTING WELL
and then feed the SICK into it, and define GETTING WELL as 1/25 times the cur-
rent level of SICK. This means that each day, 1/25
th
of the current level of SICK get
well, and therefore, roughly, the average person would be sick for 25 days. Let us
make this form of the addition first. Your model should look like this (Figure 1.14):
SICK
GETTING WELL
GETTING SICK
SICK TIME
~
CONTAGION RATE
AWARENESS LEVEL
Fig. 1.14
