Towards malaria prediction in Sri Lanka. modelling spatial and temporal variability of malaria case counts

This thesis was motivated by the need of the Anti Malaria Campaign (AMC) of Sri
Lanka for malaria risk maps and malaria case number predictions to assist in the
planning for malaria control. Despite a wealth of high resolution data collected over
decades, a malaria forecasting system was not in place, and detailed island-wide maps
of malaria incidence could permit the assessment of the malaria situation and its
determinants. The overall aim of this thesis was to describe the spatial and seasonal
distribution of malaria in Sri Lanka and associated factors, and to develop a malaria
forecasting system.
In this thesis, the spatial variation of malaria in Sri Lanka was described in relation to
risk factors. Also, the risk and the impact of a tsunami natural disaster on malaria
transmission and malaria control in Sri Lanka were evaluated. The relation in space
between seasonality of malaria and seasonality of rainfall, and the relationship
between monthly malaria case time series and monthly rainfall time series in Sri
Lanka were quantified. A model for short term malaria prediction was developed and
implemented in Sri Lanka for use by the AMC. This thesis also contributed a
statistical methodology for analysing over dispersed temporal count data with non
stationary and / or seasonal behaviour, such as observed in malaria case count time
series in Sri Lanka.
In Chapter 1, the stage was set by briefly describing malarial disease and the biology
of malarial parasites and vectors relevant to Sri Lanka. The influence of weather on
malaria transmission, and observed linkages between weather and malaria in terms of
spatial and temporal patterns were introduced. Immunity was also briefly discussed,
because it affects the translation of (unobserved) disease transmission patterns into
patterns of observed malaria cases. A brief overview was given of the history of
malaria and malaria control in Sri Lanka.
Chapter 2 provided health professionals and the larger general public with the first
island-wide incidence maps of Plasmodium vivax and Plasmodium falciparum
malaria at sub district resolution. The distribution and seasonality of P. vivax and P.
falciparum incidence was remarkably similar within each district, although they
varied spatially. The annual malaria incidence changed over the 1995 – 2002 period,
and the rate of change varied with the area, thus indicating the need for regular updates of the incidence maps. The spatial and temporal malaria distribution in the
country was related to accessibility of areas for implementation of malaria control (in
particular governed by the armed conflict and the peace process), and to socio
economic and environmental factors. Also, the exposure of tourists to malaria
infection was discussed.
Chapter 3 provided a re-assessment of the malaria situation, including details on
vector insecticide resistance, parasite drug resistance, and insights into the national
policy for malaria diagnosis and treatment. The assessment and its publication were
triggered by the tsunami that hit on 26 December 2004, and the ensuing international
concern about possibilities of an increase of vector borne diseases. The likelihood of
a widespread outbreak was estimated as limited. The public health system was
deemed capable of dealing with the possible threat of a malaria outbreak. Concerns
were expressed that the influx of foreign medical assistance, drugs, and insecticides
could interfere with malaria surveillance, and the long term malaria control strategy of
Sri Lanka, if not in accordance with government policy.
Chapter 4 assessed the impact of the tsunami on the malaria situation and the national
and international malaria control efforts in the year following the tsunami. Malaria
incidence had decreased in most districts, including the ones that were hit hardest by
the tsunami, and the whole-country malaria incidence time series did not deviate from
the downward trend that started in 2000. The focus of national and international post
tsunami malaria control efforts was supply of antimalarials, distribution of
impregnated mosquito nets and increased monitoring in the affected area.
Internationally donated antimalarials were either redundant or did not comply with
national drug policy. There was no indication of increased malaria vector density.
In Chapter 5, the spatial correlation between average seasonality of malaria and climatic seasonality of rainfall was studied. A simple index for seasonality was
developed by making use of the characteristic of a varying degree of bimodality of
seasonality present in both malaria and rainfall in Sri Lanka. The malaria seasonality
index was significantly associated with the rainfall seasonality index in a regression
taking spatial autocorrelation into account. This was in paradox with the negative
correlation in space between annual rainfall and malaria endemicity (Chapter 2). Both
rainfall and malaria may react independently to monsoonal periodicity, but given the
fact that rainfall has an important impact on the availability and quality of breeding sites for malaria vectors, it is clear that rainfall seasonality is an important driver of
malaria seasonality.
In Chapter 6, the temporal correlation between monthly malaria case time series and
monthly rainfall time series was explored for each district separately. For most
districts, strong positive correlations were found for malaria time series lagging zero
to three months behind rainfall. However, only for a few districts, weak positive (at
lags zero and one) or weak negative (at lags two to six) correlations were found if
autocorrelation and seasonality were removed from the series prior to crosscorrelation
analysis, thus indicating that rainfall might have little potential use in a
malaria forecasting system. These cross correlation analyses had the drawbacks that
inter-annual effects were masked due to detrending of the data, and that potentially
seasonally varying effects were not taken into account. Subsequent inter-annual
analysis showed strong negative correlations between malaria and rainfall for a group
of districts in the centre-west of the country. Seasonal inter-annual analysis showed
that the effect of rainfall on malaria varied according to the season (and geography).
Chapter 7 focused on the development of a malaria forecasting system for Sri Lanka,
which could assist in the efficient allocation of resources for malaria control,
especially when malaria is unstable and fluctuates in intensity both spatially and
temporally. Several types of time series models were tested in their ability to predict
the monthly number of malaria cases in districts one to four months ahead. Different districts required different prediction models, and the prediction accuracy varied with
district and forecasting horizon. It was subsequently tested if rainfall or malaria
patterns in neighbouring districts could improve prediction accuracy of the selected
models. Only for a few districts, a modest improvement was made when rainfall was
included in the models as a covariate. This modest improvement was not deemed
sufficient to merit investing in a forecasting system for which rainfall data are
routinely processed. The development and launch of a system for forecasting malaria
by the AMC was described in addendum to Chapter 7.
Throughout the statistical modelling in Chapter 7, it was assumed that logarithmically
transformed malaria case data were approximately Gaussian distributed. However,
such an approximation is less close when case numbers are low, as was the case at the
time of writing. Therefore, in Chapter 8, a class of generalised multiplicative seasonal
autoregressive integrated moving average models for the parsimonious and observation-driven modelling of non Gaussian, non stationary and / or seasonal time
series data was developed.
Chapter 9 provides a general discussion in which the contributions of this thesis are
put into context, in which limitations of this thesis are discussed and directions for
future research outlined.