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to the way chemical reactions can be specified with the law of mass action
2
—the
concentration of a chemical product (e.g. number of moles of a substance per cubic
meter air) is computed as the product of the concentrations of the reactants and
a reaction rate. Here, we convert the currently nonimmune population into a sick
population:
SICK RATE = CONTACT RATE * (CONTAGIOUS+SICK) * NONIMMUNE.
(2.1)
The structure of the complete model is shown in Figure 2.1. Initialize this
model so you have a starting populations of NON IMMUNE = 1000000,
CONTAGIOUS = 1, SICK = 0, and IMMUNE = 0. Assume a fixed number of
births of 5000 per week and a contact rate of .000002. Also, assume that individuals
who contract the disease will on average be moving around for one week before
they are bedridden and that they are contagious during that time as well as the time
during which they are confined to bed. The same contact rate applies to both subsets
of the population. Furthermore, as noted above, assume that every week 90 percent
of those sick individuals, who are confined to their beds, will recover and become
permanently immune; the remainder of them die.
The outcome for such a simple model (Figure 2.2) is interesting. It would be
difficult to predict that the simple equation for GET SICK would yield the remark-
ably authentic series of diminishing pulses. In many ways, the appearance of these
pulses is an emergent property of the model, and it is realistic. The initial epidemic
is the most severe and converts 90% of the population to an immune condition.
NON IMMUNE
CONTAGIOUS
BIRTHS
STAY IN BED
GET SICK
CONTACT RATE
IMMUNE
RECOVER
DIE
SICK
Fig. 2.1
2
See, for example, Hannon, B. and M. Ruth. 2001. Dynamic Modeling, 2
nd
Edition, Springer
Verlag, New York.
