Page 258 - DCAP601_SIMULATION_AND_MODELING

Simulation and Modelling

Notes little effect on prevalence data in this context, though as one would expect, the further the
initially-infected proportion(s) from the bounds within which the later prevalence stabilize, the
greater the range(s) of earlier oscillations. As discussed below, the results are also valid for a
range of vector population sizes and interaction frequencies.
In the context of perennial single-strain transmission, the parameter ranges considered here
lead to human prevalence of 50 % to 85%, a typical range in several tropical regions. Recent
results with PCR-based detection methods indicate that these high prevalence are even more
common than had been assumed based on surveys using conventional microscopy. Our results
show that, as expected under such conditions, prevalence in humans increases as mosquito
survivorship increases (as in Macdonald’s model).

Notes The prevalence in vectors increases as either the period of host infectivity or the
rate of host immune decay increases.

Results – Vector Population Size

It has long been recognized that the differing degrees of anthropophily among Anopheles
species convolve with relationships between mosquito lifespan, parasite development cycles
and other factors such that at any given moment a relatively small fraction of a mosquito
population actually contributes to the transmission of malaria in a human population. Our
models not only manifest similar behavior, but do so in a manner that allows quantification and
scaling of the vector population required to maintain several key epidemiologic characteristics
of infection in a given human population. All else being equal, maintaining a constant prevalence
of infection in humans and a constant number of infectious mosquito bites per human per day
requires a total number of mosquito bites per day, V , that scales less than linearly with the total
B
mosquito population size, N . That is, some of the effects of enormous populations of vectors
V
may be modeled without fully representing each constituent, such that it may be possible to
consider “effective” vector population sizes in epidemiological as well as population-genetic
terms.

Figure 13.6 plots prevalence isoclines for two extremes of mosquito survivorship, showing the
joint values of V and N equivalent to a population of 5,000 mosquitoes feeding only on the
B V
given human population, with an idealized blood meal cycle (N /V ) of two days. That is, in
V B
terms of the prevalence of infection in humans and the number of infectious mosquito bites per
human per day in this context, 5,000 is the “effective” mosquito population size of each of these
<N , V > combinations. The six <N , V > points shown for each parameter set closely follow an
V B V B
b
exponential (power-law) function, V = aN . Equivalently, for a given human population size
B V
and number of daily mosquito bites, the scaling formula N = (V /a) (1/b) approximates all
V B
population sizes of mosquitoes synonymous in key epidemiological terms with a given
population size of mosquitoes biting only humans; other population sizes imply zooprophylaxis
or different gonotrophic cycles. We estimated values for the constants a and b using Systat 4.0
(Systat Inc., Evanston, IL), and found that maintaining constant “effective” vector population
sizes requires that the total number of daily host-vector interactions increase by less than the
square root of the total vector population size.

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