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and adults. The model has two parts, one for the healthy population and one for
the diseased population. Diseased nymphs can infect healthy nymphs and become
diseased adults. Diseased adults cannot infect healthy adults or nymphs but can pro-
duce infected nymphs. Note how these features are expressed in the model by the
appropriate flows and links.
Assume that the infection coefficient is based on an exponential model:
INFECTION COEF
=
1
−
EXP
(
−.
3
∗
NYMPHS
∗
NYMPHS D
)
(3.7)
NYMPHS and NYMPHS D refer to the population sizes of healthy and infected
nymph populations, respectively. The INFECTION RATE is calculated as the prod-
uct of the INFECTION COEF, the number of healthy nymphs, divided by the model
maturation rate for survivors, MNSF/TN
INFECTION RATE
=
MNSF/TN
∗
INFECTION COEF
∗
NYMPHS
(3.8)
with
MNSF
=
Model Nymph Survival Fraction
(3.9)
=
EXP(LOGN(ENSF)/TN
∗
DT
)
where TN is the experimental nymph maturation rate and ENSF is the dimensionless
experimental nymph survival fraction. When there are no sick nymphs or healthy
nymphs, the probability of becoming infected equals zero. The specification of the
INFECTION COEF translation variable is a purely empirical formulation but it
gives the correct value at the extremes: 0 when the number of diseased nymphs
is zero or when the number of healthy nymphs is zero, and near 1 when either at
least one of the stocks NYMPHS or NYMPHS D is very large.
Note well the specification of the MATURING function in the model, which en-
sures that the total rate of change from nymphs to adults here is still U1*NYMPHS:
MATURE
=
MNSF/TN
∗
NYMPHS
∗
(
1
−
INFECTION COEF
)
(3.10)
Figure 3.4 shows the proportions of healthy nymphs and adults, and the number
of diseased nymphs and adults. Similar to the previous section of this chapter, we
find distinct phases for the outbreak of a disease.
These newly diseased nymphs are converted to diseased adults rather than
directly into diseased nymphs in an effort to reflect the fact that these nymphs, who
contract rather than acquire the disease, have the normal nymph survival rate. In
addition, they are unable to convey the disease to other healthy nymphs.
