Page 257 - DCAP601_SIMULATION_AND_MODELING

Unit 13: Simulation Languages (I)

Notes

Did u know? What is parasite transmission?

Parasite transmission is represented as a single state-altering interaction between an
individual host and an individual vector.

Parameter Values and Initial Conditions

Figure 13.6 shows the typical pattern of damped oscillations in prevalence for the wide ranges
of parameter values and initial conditions considered here. The results presented in this paper
are from data collected every tenth day during the last 100 days of 365-day runs. Because varying
the delay parameters in this context leads to phase differences with little effect on such prevalence
data, we generally fixed D = 20 and D = 10, then examined the relative influence of the
H V
remaining temporal parameters on prevalence by systematically varying these parameter values
within a large plausible subspace. We most closely examined parameter values over a range
from 50% to 150% of a plausible mean value for each, such that the values of the host window
(WN) ranged from 10 to 30 days, vector half-life from 5 to 15 days (i.e., VS from 0.954 to 0.861),
and host immunity half-life from 50 to 150 days (i.e., IM from 0.014 to 0.005). For each <VS, WN,
IM> point, we performed 100 replicate runs; standard deviations in prevalence about each of the
mean <VS, WN, IM> points used in our analyses were <0.01. We used Mathematical 2.0 (Wolfram
Research, Champaign IL) to obtain best-fit planes to surfaces of 231 prevalence points for each
pair-wise combination of parameters at five levels of the third parameter.

Figure 13.6

In Figure 13.6, an example of the time course of the overall malaria prevalence (solid line) and
of the prevalence of infectious stages (dashed line) in a human population, demonstrating
damped oscillations. The levels and rates at which prevalence stabilize depend.
We generally set N = 5000 and V = 2500, in accord with the usual idealized two-day geotropic
V B
cycle for Anopheles (i.e., N /V = 5000/2500), and set N = 500 (i.e., N /N = 10), with 25% of the
V B H V H
hosts and none of the vectors initially infected. Varying the proportion(s) initially infected had

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