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negativity described above informed the model of the fraction of Duffy-
negative individuals in the population at each pixel of the predicted sur-
face. The parasite endemicity prediction could be made, therefore, from the
vivax-susceptible or Duffy positive portion of the population. This meant
that the proportion of
Pv
PR could not exceed the percentage of the popu-
lation who were Duffy positive and that predictions in data-sparse portions
of Africa could borrow strength from the Duffy negativity surface because
estimates were limited to a more restricted range of potential outcomes.
The endemicity surface that results from the MBG modelling frame-
work described is a 5 × 5 km grid of predictions for
Pv
PR
1-99
within
the limits of stable
P. vivax
transmission. For practical reasons, and because
areas endemic for
P. vivax
have distinct ecological, entomological and epi-
demiological characteristics, the
P. vivax
endemic world was divided into
four regions: the Americas, Africa+, Asia and Asia-Pacific. Separate models
were fitted to each region so that a
Pv
PR
1-99
estimate averaged across the
12 months of 2010 was found. The endemicity map was created by using
the mean of each posterior distribution as a point estimate and uncertainty
was shown as the ratio of the posterior distribution IQR to its mean. The
IQR was found to express the precision with which the
Pv
PR
1-99
values
were predicted. Calculation of the ratio of the IQR of each posterior dis-
tribution to its mean generated an index that demonstrated how the model
performance varied with data density in different locations. This index was
also weighted by population density to generate a map to show where high
levels of uncertainty may be operationally significant.
6.3. The Refined Population at Risk of
P. vivax
The various data sources described above were combined to produce the
final spatial limits map (
Fig. 1.10
A6-D6). After the implementation of
MBG modelling, some of the regions that were estimated as being within
the limits of stable transmission were downgraded to unstable transmission.
If the model outputs of
Pv
PR were extremely low due to a large abundance
of surveys reporting zero infections in that area or, in Africa, because of
high Duffy negativity, a decision rule was applied such that pixels that were
predicted with high certainty (probability >0.9) to be less than 1%
Pv
PR
were reassigned as unstable.
The PAR of
P. vivax
malaria was estimated using the constrained limits
of infection and population values for 2010 projected from the year 2000
GRUMP
beta
version population counts. The result was a 1 × 1 km spa-
tial grid of population surface of the number of people living at stable or
