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CPS1952 Michele N. et al.
an arbitrary number of von Mises components can be used, we only use two
because areas with seasonal malaria transmission typically have one or two
main seasons (Stuckey et al. 2014).
Based on the fitted R2vM curve, we identify the transmission periods by
marking the months where the curve is at or above 1/12. In this way, we can
also obtain the start, end and length of each season. If there is only one
transmission period, we fit a rescaled, one component von Mises density to
the monthly proportions and estimate the seasonality statistics based on this
instead.
To obtain the uncertainty associated with the derived statistics, we
summarise the results from 100 posterior samples of the monthly proportions.
By looking at the proportion of times a location is deemed bimodal or
unimodal, we can obtain the majority decision as well as the degree of
certainty. Based on this, we can analyse the uncertainty in the estimated
seasonal characteristics. For the start, end and length of the transmission, we
can obtain the means and standard deviations.

2.4. Adjusted seasonality index
The seasonality index introduced in Section 2.1 does not work well for
bimodal distributions since the entropy does not account for the two peaks
and only considers the overall distribution in a year which typically appears as
more even than a unimodal one. To better reflect the degree of seasonality,
we adapt the entropy for bimodal distribution at location using the fitted
R2vM function as follows:

̃
= (1) + (1 − ) (1) ,

12 (, , )
ℎ () = ∑ (, , ) ( )
2

=1

for =1,2 and the terms are as defined before. For consistency, we also base
the adjusted seasonality index for unimodal distributions on the fitted one
component von Mises density.

3. Results
We illustrate our method using case data from the LAC region and restrict
our analysis to Plasmodium vivax (Pv), the dominant malaria species there. We
study the smallest administrative units available over each area and use their
centroid coordinates as their point locations.
For the years 2009-2016, we can compute monthly median case counts for
1 ADMIN1 (state) unit and 567 ADMIN2 (municipalities) units in Brazil, 458

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