# Spatial and temporal patterns of malaria incidence in Mozambique.

**ABSTRACT** The objective of this study is to analyze the spatial and temporal patterns of malaria incidence as to determine the means by which climatic factors such as temperature, rainfall and humidity affect its distribution in Maputo province, Mozambique.

This study presents a model of malaria that evolves in space and time in Maputo province-Mozambique, over a ten years period (1999-2008). The model incorporates malaria cases and their relation to environmental variables. Due to incompleteness of climatic data, a multiple imputation technique is employed. Additionally, the whole province is interpolated through a Gaussian process. This method overcomes the misalignment problem of environmental variables (available at meteorological stations--points) and malaria cases (available as aggregates for every district--area). Markov Chain Monte Carlo (MCMC) methods are used to obtain posterior inference and Deviance Information Criteria (DIC) to perform model comparison.

A Bayesian model with interaction terms was found to be the best fitted model. Malaria incidence was associated to humidity and maximum temperature. Malaria risk increased with maximum temperature over 28 °C (relative risk (RR) of 0.0060 and 95% Bayesian credible interval (CI) of 0.00033-0.0095) and humidity (relative risk (RR) of 0.00741 and 95% Bayesian CI 0.005141-0.0093). The results would suggest that additional non-climatic factors including socio-economic status, elevation, etc. also influence malaria transmission in Mozambique.

These results demonstrate the potential of climate predictors particularly, humidity and maximum temperature in explaining malaria incidence risk for the studied period in Maputo province. Smoothed maps obtained as monthly average of malaria incidence allowed to visualize months of initial and peak transmission. They also illustrate a variation on malaria incidence risk that might not be related to climatic factors. However, these factors are still determinant for malaria transmission and intensity in the region.

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- Martin Walker, Peter Winskill, María-Gloria Basáñez, Joseph M Mwangangi, Charles Mbogo, John C Beier, Janet T Midega[Show abstract] [Hide abstract]

**ABSTRACT:**The distribution of anopheline mosquitoes is determined by temporally dynamic environmental and human-associated variables, operating over a range of spatial scales. Macro-spatial short-term trends are driven predominantly by prior (lagged) seasonal changes in climate, which regulate the abundance of suitable aquatic larval habitats. Micro-spatial distribution is determined by the location of these habitats, proximity and abundance of available human bloodmeals and prevailing micro-climatic conditions. The challenge of analysing-in a single coherent statistical framework-the lagged and distributed effect of seasonal climate changes simultaneously with the effects of an underlying hierarchy of spatial factors has hitherto not been addressed. Data on Anopheles gambiae sensu stricto and A. funestus collected from households in Kilifi district, Kenya, were analysed using polynomial distributed lag generalized linear mixed models (PDL GLMMs). Anopheline density was positively and significantly associated with amount of rainfall between 4 to 47 days, negatively and significantly associated with maximum daily temperature between 5 and 35 days, and positively and significantly associated with maximum daily temperature between 29 and 48 days in the past (depending on Anopheles species). Multiple-occupancy households harboured greater mosquito numbers than single-occupancy households. A significant degree of mosquito clustering within households was identified. The PDL GLMMs developed here represent a generalizable framework for analysing hierarchically-structured data in combination with explanatory variables which elicit lagged effects. The framework is a valuable tool for facilitating detailed understanding of determinants of the spatio-temporal distribution of Anopheles. Such understanding facilitates delivery of targeted, cost-effective and, in certain circumstances, preventative antivectorial interventions against malaria.Parasites & Vectors 01/2013; 6(1):311. · 3.25 Impact Factor - SourceAvailable from: Ogobara K DoumboDrissa Coulibaly, Stanislas Rebaudet, Mark Travassos, Youssouf Tolo, Matthew Laurens, Abdoulaye K Kone, Karim Traore, Ando Guindo, Issa Diarra, Amadou Niangaly, Modibo Daou, Ahmadou Dembele, Mody Sissoko, Bourema Kouriba, Nadine Dessay, Jean Gaudart, Renaud Piarroux, Mahamadou A Thera, Christopher V Plowe, Ogobara K Doumbo[Show abstract] [Hide abstract]

**ABSTRACT:**BACKGROUND: Heterogeneous patterns of malaria transmission are thought to be driven by factors including host genetics, distance to mosquito breeding sites, housing construction, and socio-behavioural characteristics. Evaluation of local transmission epidemiology to characterize malaria risk is essential for planning malaria control and elimination programmes. The use of geographical information systems (GIS) techniques has been a major asset to this approach. To assess time and space distribution of malaria disease in Bandiagara, Mali, within a transmission season, data were used from an ongoing malaria incidence study that enrolled 300 participants aged under six years old". METHODS: Children's households were georeferenced using a handheld global position system. Clinical malaria was defined as a positive blood slide for Plasmodium falciparum asexual stages associated with at least one of the following signs: headache, body aches, fever, chills and weakness. Daily rainfall was measured at the local weather station.Landscape features of Bandiagara were obtained from satellite images and field survey. QGISTM software was used to map malaria cases, affected and non-affected children, and the number of malaria episodes per child in each block of Bandiagara. Clusters of high or low risk were identified under SaTScan(R) software according to a Bernoulli model. RESULTS: From June 2009 to May 2010, 296 clinical malaria cases were recorded. Though clearly temporally related to the rains, Plasmodium falciparum occurrence persisted late in the dry season. Two "hot spots" of malaria transmission also found, notably along the Yame River, characterized by higher than expected numbers of malaria cases, and high numbers of clinical episodes per child. Conversely, the north-eastern sector of the town had fewer cases despite its proximity to a large body of standing water which was mosquito habitat. CONCLUSION: These results confirm the existence of a marked spatial heterogeneity of malaria transmission in Bandiagara, providing support for implementation of targeted interventions.Malaria Journal 03/2013; 12(1):82. · 3.40 Impact Factor

Page 1

RESEARCHOpen Access

Spatial and temporal patterns of malaria

incidence in Mozambique

Orlando P Zacarias1,2*and Mikael Andersson3

Abstract

Background: The objective of this study is to analyze the spatial and temporal patterns of malaria incidence as to

determine the means by which climatic factors such as temperature, rainfall and humidity affect its distribution in

Maputo province, Mozambique.

Methods: This study presents a model of malaria that evolves in space and time in Maputo province-Mozambique,

over a ten years period (1999-2008). The model incorporates malaria cases and their relation to environmental

variables. Due to incompleteness of climatic data, a multiple imputation technique is employed. Additionally, the

whole province is interpolated through a Gaussian process. This method overcomes the misalignment problem of

environmental variables (available at meteorological stations - points) and malaria cases (available as aggregates for

every district - area). Markov Chain Monte Carlo (MCMC) methods are used to obtain posterior inference and

Deviance Information Criteria (DIC) to perform model comparison.

Results: A Bayesian model with interaction terms was found to be the best fitted model. Malaria incidence was

associated to humidity and maximum temperature. Malaria risk increased with maximum temperature over 28°C

(relative risk (RR) of 0.0060 and 95% Bayesian credible interval (CI) of 0.00033-0.0095) and humidity (relative risk (RR)

of 0.00741 and 95% Bayesian CI 0.005141-0.0093). The results would suggest that additional non-climatic factors

including socio-economic status, elevation, etc. also influence malaria transmission in Mozambique.

Conclusions: These results demonstrate the potential of climate predictors particularly, humidity and maximum

temperature in explaining malaria incidence risk for the studied period in Maputo province. Smoothed maps

obtained as monthly average of malaria incidence allowed to visualize months of initial and peak transmission.

They also illustrate a variation on malaria incidence risk that might not be related to climatic factors. However,

these factors are still determinant for malaria transmission and intensity in the region.

Background

Malaria is considered one of the most deadly diseases in

Mozambique, with around six million cases reported

each year [1]. Most of these cases are Plasmodium falci-

parum [1,2]. Transmission takes place all year round

with a seasonal peak extending from December to April.

Many factors affect the dynamics of malaria transmis-

sion and infection, ranging from social to natural. Rain-

fall and temperature can be considered the major

natural risk factors affecting the life cycle and mosquito

breeding [2]. Relative humidity plays a role in the life-

span of the mosquito. In the presence of high relative

humidity values, the parasite would complete the neces-

sary life cycle in order to increase transmission of the

infection to more humans. All districts in Maputo pro-

vince show favourable climatic conditions for develop-

ment and transmission of malaria [3]. Studies on

prevalence of malaria are important not only to assess

the problem of malaria in a given region, but also to

analyse the effectiveness of strategies for primary and

secondary prevention, as well as its quality and impact.

A combination of advances in hierarchical modelling

and geographical information systems has led to the

developments in fields of geographical epidemiology and

public health surveillance. This made it possible to

explore and characterize different sets of spatial disease

patterns at a very fine geographical resolution [4]. As a

result, disease mapping has been widely used in

* Correspondence: si-opz@dsv.su.se

1Department of Mathematics and Informatics (DMI), Eduardo Mondlane

University, Maputo, Mozambique

Full list of author information is available at the end of the article

Zacarias and Andersson Malaria Journal 2011, 10:189

http://www.malariajournal.com/content/10/1/189

© 2011 Zacarias and Andersson; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative

Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and

reproduction in any medium, provided the original work is properly cited.

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epidemiology and public health research [5]. The use of

geographical mapping helps the detection of areas with

high disease incidence for which usually neighbouring

areas show similar factors. One common application of

disease mapping has been in describing the variation in

health outcomes over geographic regions. However,

mapping of crude disease rates can be quite misleading

particularly at a small area level. This is often due to the

combination of two factors: small regional incidence

counts and the presence of spatial correlation in the

rates. Low prevalence diseases do not provide a possibi-

lity of obtaining stable estimates at the district level. For

high prevalence diseases like malaria however, these

estimates are easily attained due to the availability of a

large amount of information at the district level.

Different approaches have been used to model spatio-

temporal problems, starting from work by [6] in which

space-time interaction is realized by assuming area-speci-

fic linear time trend for relative risks. Many other

researchers [7,8] proposed and implemented space-time

models with different interactions. Spatial and temporal

malaria variation is studied in [9] with an investigation of

possible geographical expansion of malaria transmission.

Space-time models using malaria data are investigated in

research by [10,11] where they use dynamic and Bayesian

models respectively. Climatic variables are then used as

covariate predictors of malaria incidence risk.

This study is motivated by the need to investigate the

spatial and temporal variation in malaria rates at the

district level in Maputo province - Mozambique, for the

period 1999-2008. It is postulated that malaria incidence

rates are highly influenced by environmental factors that

vary in space and time. To establish this influence, a

Bayesian hierarchical model relating malaria incidence

rates and climatic data is formulated. The analysis looks

at possible relationships between environmental factors

and malaria rates to learn about spatial and temporal

similarities amongst these rates on different districts of

Maputo province. It is expected that the model will

facilitate the mapping and elucidation of spatio-temporal

patterns of malaria incidence risk. However, before

employing environmental factors to explain malaria inci-

dence two issues need to be considered first:

1. The problem of incomplete data, i.e. missing of

some explanatory variables. Multiple imputation

approach to missing data is pursued.

2. Gelfand et al [12] define the change of support

problem (COSP) as relating to the inference about

the values of a variable measured at different levels

of spatial aggregation from those at which it has

been observed. In this study, the COSP is addressed

by interpolating these factors (covariates) through a

Gaussian process.

The aims of this investigation are:

(a) To provide a spatio-temporal analysis of malaria

incidence risk;

(b) To determine the contribution of predictors/cov-

ariates in the variation of malaria incidence risk

Methods

Study area and data

Given the wide geographic range of Mozambique and

weakness of health information system in other regions

of the country, a particular region less comprehensive

than the whole country was chosen with better quality

systems of health recording. Maputo province is located

in south of Mozambique with an estimated area of

23,669 square kilometres. Eight administrative districts

comprise the province and are shown in the map of

Figure 1. Detailed description of study area is given else-

where [3].

The data comprises malaria rates and environmental

averages of rainfall, temperature (minimal, average and

maximum) and relative humidity for years 1999-2008 in

each month. In fact, the environmental data are avail-

able as monthly averages at each monitoring station

obtained through the National Institute of Meteorology

(INAM), and the response is available as monthly counts

of malaria cases in each district. Malaria data includes

records from health posts and centres, and rural hospi-

tals compiled at district level in Maputo province [3].

These counts are registered daily and used to generate

Figure 1 Study region.

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Weekly Epidemiology Bulletin. It includes both micro-

scopically and clinically confirmed cases. They are col-

latedandsummarized

department and reported to provincial health Officers’

monthly. The summaries are than sent to the Ministry

of Health and shared with different disease control pro-

grammes. Expected malaria cases are taken as the num-

ber of people in each district according to population

projections of 1997 and 2007 national census. Figures 2

and 3, illustrate the variation of malaria cases for years

with highest and lowest frequency respectively.

byeachdistrict health

Modelling

Environmental data used in this study is collected at

monitoring stations located in five out of eight districts

in Maputo province. This a typical situation of change

of support (misaligned) problem with environmental

factors observed at fixed locations s (point referenced

data), whereas the malaria cases are observed at district

level. Different approaches are proposed by Zhu and

colleagues [12] to tackle the problem of misaligned,

namely: predictions from points to points, points to

blocks and blocks to blocks. Their work is supported by

an application to a static spatial case using the dataset

of point-level ozone measurements in the Atlanta

metropolitan area. Same researchers in [13] investigated

further, by looking at the relationship between ambient

ozone and paediatric emergency room visits. The appli-

cation is extended to spatio-temporal model with log-

ozone modelled by a stationary Gaussian process. Before

Figure 2 Variation of monthly malaria cases per district. Highest malaria trend year 2000.

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attempting to model misaligned data it was necessary to

address the problem of missing data.

A. Modelling environmental data

A.1 Missing data imputation In the process of data

analysis, it is commonplace to observe that data for each

case are not always complete. Rather, some data are

usually missing. The amount of missing data may be

minimal for some cases; in others perhaps significant.

Problems dealing with the analysis of missing data have

been extensively reviewed in the scientific literature

[14-16]. Environmental time series generally have as

their main focus physical and chemical measurements.

Hence, problems such as reserved information, privacy

respect and non-response as for example in social and

medical surveys are not present. The main sources of

missing records considered in this study are:

• Break-down of measurement instruments;

• Maintenance interventions, and

• Reading invalidation.

Thus, the data was analysed assuming missing at ran-

dom mechanism with an incomplete level of environ-

mental observations of around 16.7%. Multiple

imputation (MI) package in R [17] was used to perform

the imputation of m = 5 values for each missing record

hence creating five complete datasets. The five imputed

values on each variable of interest were aggregated to

Figure 3 Variation of monthly malaria cases per district. Lowest malaria trend, year 2007.

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produce inferential results. The single point estimate

was attained by averaging the values of parameter esti-

mates for the covariates rain, humidity and temperature

(maximum, mean and minimal values). Table 1 shows

the variation and mean of each imputed environmental

covariate obtained through MI.

In the execution of space-time model with one

imputed data set, the results obtained for the main para-

meters were similar to the run of the model with the

data obtained as average values of the five datasets. This

assures us that the procedure applied for MI produced

consistent results.

A.2 Misaligned problem The change of support pro-

blems of interest includes predicting rain, temperature

(minimum, mean and maximum) and relative humidity

measurements at different points on the map and from

that moving to prediction of average weather parameters

at district level. Although there are at least twenty-six

weather stations registered in Maputo province, on aver-

age only five or six stations are operational at any time.

The sites are daily monitored within the same time

interval and data is aggregated for every four weeks

(month). Hence, it comprises time series of spatial pro-

cesses as the time scale is equally spaced. It is reason-

able to consider the change of support problem only in

space [13].

Assuming continuous observations from a spatio-tem-

poral process denoted by Z(s, t) at time t ε T and location

s ε D, we seek to change support from observed points to

district (block) averages. Following the approach

employed in [13], the block average is defined as,

?

B

Z(B,t) = |B|−1

Z(s,t) dx

(1)

where |B| is the area of block B ⊂ D. Each point in

Maputo province is described by its latitude and longi-

tude coordinates through a spatial random field {Z(s):s

Î D}, where D ⊂ ℜpand p = 2. The amount of rainfall,

temperature and humidity Zt(B1), ..., Zt(Bm) ≡ Z1t, ...,

Zmtis predicted for each time t (month) in all districts.

To obtain predictors for each district (block) Bi, a 90-

point grid is overlaid over Maputo province map and

the integral in (1) was approximated to a sum. The

interpolation is performed by applying Bayesian kriging.

Following [4], the random field has to be Z = Z(s1), ..., Z

(sn) predicted at non-observed point s0. The model is

specified as,

Z = Xβ + ε,where ε ∼ N(0,?)

A spatial covariance structure with no nugget effect is

used, with Σ specified as Σ = s2H(j) where (H(j))ij= r

(j; dij). Being the dij= || si- sj|| distance between

points siand sjand r is an ordinary exponential func-

tion. To complete model specification independent

priors are assigned to the parameters namely, a multi-

variate normal for b, inverse gamma for s2with para-

meters a = 0.004 and b = 0.02, and a gamma prior for j

with mean 0.12 and variance about 0.05. The amount of

each environmental factor predicted in every district i

was estimated as the mean of the posterior predictive

distribution of the random field process at points of the

grid that have fallen within that district. This procedure

was independently repeated for every year r = 1999, ...,

2008.

B. Modelling malaria risk in space and time

As a result of preliminary bi-variate analysis performed

in statistical package R, the explanatory covariates tem-

perature (minimal, mean and maximum), rainfall and

humidity showed a significant relationship p < 0.001

with malaria incidence (Table 2). The data consists of

observed malaria counts Oritand expected cases Eriin

districts i = 1, ..., M (M = 8), for year r = 1, ..., Years

(Years = 10) and month t = 1, ..., T(T = 12) in Maputo

province.

Counts of malaria are registered daily at different

health centres and rural hospitals generating Weekly

Epidemiology Bulletin. They are collated and summar-

ized by each district government health department and

reported to provincial health Officers’ monthly. These

summaries are sent to the Ministry of Health and shared

with different disease control programmes. Expected

cases are taken as being the population of each district

in a corresponding year.

Malaria observed counts are assumed to follow a Pois-

son distribution with mean μrit. The log-relative term

modelling all predictor data variables is written as,

(2)

log(μrit) = log(Pri) + α + βTXrit+ θi+ ϕrt+ δrit

(3)

Table 1 Overall estimated mean and variance of imputed

data.

EstimatedRainMax-

Temp

Min-

Temp

Mean-

Temp

Humidity

Mean73.0829.4417.0823.2369.16

Variance3957.741.8614.9343.2119.586

Table 2 Results of bi-variate analysis of prediction

variables.

CovariateCoefficientSEP-value

Min-Temp

Mean-Temp

Max-Temp

Rainfall

Humidity

.078

.0694

.0558

.001

.0742

.0001

.0002

.0002

.000006

.00014

< .001

< .001

< .001

< .001

< .001

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where a is a measure of overall incidence (intercept

term), θiis the spatial random effect and ?rtis the

monthly temporal random effect for each year. δritis

defined as space and time interaction term with b and

Xritbeing vectors of regression coefficients and environ-

mental covariates respectively. The spatial dependence is

introduced through the conditional autoregressive

(CAR) process.

In the CAR model, the conditional distribution of each

θigiven all other θ’s is a normal distribution with mean

equal to the average of θ’s of its neighbours, and preci-

sion proportional to the number of neighbours. Hence,

a neighbourhood structure needs to be defined and sup-

plied to the model through matrix W. This matrix is

important as it specifies how much influence neighbour-

ing districts will have on district i. Figure 1, illustrates

the location of each district where can be noticed that

the shapes and the lengths of their boundaries vary

quite a bit among districts.

One simple way to take this information into account

is to assign different weights to neighbouring districts

according to the length of their boundaries. Therefore,

two different specifications of the weighting matrix W

are used:

1. Binary structure with ωij= 1 for neighbouring dis-

tricts i and j, and ωij= 0 otherwise;

2. Weighted by the length of the boundary, i.e. with

ωijequal to the border length (in km) for districts i

and j, and ωij= 0 for districts not sharing common

boundary. In this case the effect of neighbouring dis-

trict varies according to the extension of its

boundary.

To capture local dependence in time, the year and

month temporal trends ?rtwere given a first order ran-

dom walk prior that allows for year independence. This

is a simply one dimensional version of the CAR Normal

prior distribution. Hence,

ϕrt∼ CARNormal(Q,σ2

and the weight matrix Q defines the temporal neigh-

bours of month t as being months t-1 and t+1 for t = 2,

..., 11; with months t = 1 and t = 12 having singular

neighbours.

The space-time interaction terms δritcapture depar-

ture from space and time main effects which may high-

light space-time clusters of malaria risk. In the present

study they are assumed to be independent for every year

and month with a constant variance over time. This is

captured by an auto-regressive AR(1) prior process. It is

parameterized by a temporal variance σ2

correlation between consecutive months within the

ϕ)

(4)

δthat allows for

same district, i.e. assumes that cases at month t are

influenced by cases of month t-1. This relationship

holds for months in same year and also for December-

January relation of consecutive years, except for January

in first and December in last year. A uniform prior was

specified to the intercept term and a standard normal

prior for coefficients b with high variance. Spatial and

temporal random effects variance parameters were spe-

cified inverse gamma hyper-prior distributions.

The covariate mean temperature was removed from

the analysis as it is in general highly correlated with cov-

ariate values of maximum and minimum temperatures

respectively. However, it was felt necessary to introduce

into the analysis the influence of temperature variation

on the incidence of malaria, which is modelled by the

differences of maximum and minimum temperatures at

each time point. Humidity, minimal and maximum tem-

perature showed non-linear relationship to log(Orit) and

were converted to categorical variables for further analy-

sis. Hence, to isolate outliers from the analysis and

allow for better observation of the linearity relationship

between the variables of the model, the plotting of log-

transformed climatic covariates against the ratio of

malaria prevalence and population was performed. Their

scatter plots are shown in Figure 4. Cut-off points were

determined using the statistical package R, with the

superimposition of graphs of predictors and the distri-

bution of the ratio of malaria cases and population. For

points that did not appear on the × axis, the minimum

and/or maximum values (inflection points) were deter-

mined, taking also into consideration the change of con-

cavity of the graph. This resulted into having ten

coefficients for different threshold intervals with outliers

being disregarded.

Model fitting used Markov Chain Monte Carlo

(MCMC) simulation techniques implemented in Win-

bugs with employment of two parallel consecutive

chains. A burn-in of 30,000 iterations was allowed

where values of main parameters were stored. Diagnos-

tic tests for convergence of stored variables were under-

taken, including the analysis of the Brooks, Gelman and

Rubin statistics and visual examination of history and

density plots, and by computing Monte Carlo errors

(MCE). The value MCE/SD was less than 0.05 and thus

concluded that sufficient iterations had been conducted.

This was followed by a further 30 000 iterations run to

obtain posterior distributions of the parameters.

Results

On average, 324,014 malaria cases were reported per

year. Although displaying cases of malaria incidence for

just two years, the skewness of malaria data in time ser-

ies plotted in Figures 2 and 3 is apparently evident.

Therefore, there was a need to generate and model

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smoothed estimates disease risk in order to extract

important features from the data. Seven different models

were initially analysed following equation (3) and a com-

parison of their appropriateness performed. This led to

dropping of purely temporal structure as being non-

important according to its Deviance Information Criteria

value [18]. Further refinement considered was the omis-

sion of spatio-temporal effect. This resulted into a non-

converging spatial model. Table 3 gives the final consid-

ered set of models. The DIC analysis shows that model

Bwas found to be the best fitted model. Thus, results

presented are based on this fitted model.

Table 4 shows the regression coefficients of the space-

time model where it can be seen that rainfall, minimum

temperature in the range 11 to 16.4 and maximum tem-

perature in the range 24.5 to 27 degrees centigrade are

not associated with incidence risk of malaria in the per-

iod under study. However, values of minimum tempera-

ture between 17 and 21.1°C, maximum temperature of

28 to 35°C and the occurrence of relative humidity in

the range 54.5% to 83% determined positive association

with malaria risk. Maximum temperature and humidity

in the same range contributed significantly to malaria

incidence. Furthermore, an increase of 1°C of maximum

temperature leads to higher increase of malaria

Figure 4 Illustration of linear relationship of covariates versus malaria cases in log scale. Piecewise intervals of climatic factors.

Table 3 Comparison of fitted models.

Model DescriptionWeight structure DIC

(A) - Full model

(B) - Full model

(C) - Non-spatial

Border lengths

Binary adjacency

None

10714.8

10711.8

10719.5

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incidence risk. Whereas, an increase of 1% of relative

humidity leads to a variation of malaria from lower to

higher incidence risk.

The effect of humidity and maximum temperature on

malaria incidence risk is very high as illustrated by their

mean posterior predictive P-value in Table 4. The mean

P-value decreases below the critical values as the maxi-

mum temperature levels increases. For humidity predic-

tor the mean P-value shows similar pattern. The values

estimated by a posterior Bayesian model show a marked

variation compared to the Standard Mortality Ratio as

shown on maps (See Additional files 1 and 2). There are

no similarities in general for regions with both higher

SMR and estimated malaria risk. It can be seen that for

the months of May to July malaria incidence is very

stable. The trends of incidence in the districts of Matu-

tuine and Namaacha are generally lower compared to

other districts except for August where this trend

increases in the district of Namaacha. For the district of

Namaacha, this could particularly be due to being

located at higher altitude compared to other districts.

Most of its administrative posts lie 400 meters above sea

level while the other districts are around 50 meters and

surrounded by several water basins. The model using

border lengths for weighting matrix did not improve

model performance as it is shown by results of DIC ana-

lysis in Table 3. It only over-performed the model with

no spatial dependency, i.e. non-spatial model.

Discussion and conclusions

This research have analysed malaria cases data from

spatio temporal perspective to identify significant pre-

dictors associated with malaria incidence risk and to

produce contemporary smoothed maps of disease risk in

Maputo province. Maps of smoothed space-time malaria

incidence have been produced in several studies [9-11].

Besides the application of techniques of data multiple

imputation and spatial alignment in a typical problem

analysing the incidence of malaria in Mozambique, this

study implements the Bayesian models for analysis with

inclusion of temporal random effects and space-time

interaction terms.

The problem of missing data is a major issue during

the analytical process of any study. This is normally

addressed by applying imputation techniques. They fol-

low into two categories: single imputation and multiple

imputations (MI). The first has been subjected to

increasing criticism by researchers due to its tendency

of introducing bias and underestimating standard errors

[19]. However, if the quantity of missing values is very

small (less than 5%) this methodology can in general be

considered accurate. The procedure of multiple imputa-

tions is a more general method for inference with miss-

ing data. It replaces each missing record with multiple

plausible values instead of a single replacement of miss-

ing observation.

The mechanism of missing data relates to the underly-

ing reason why the data are actually missing and may

follow into three categories [20]:

1. Missing Completely at Random (MCAR): in terms

of analysis, no difference established between miss-

ing and not missing cases.

2. Missing at Random (MAR): missing data is fully

described by variables observed in dataset.

3. Missing Not at Random (MNAR): data missing in

an unmeasured fashion termed “non-ignorable”

The establishing of main source of missing records

helped to determine and identify the MAR as the most

appropriated missing data mechanism underlying the

environmental data incompleteness in this study.

The spatial pattern of malaria showed that to the

north of Maputo province there is a more pronounced

pattern of incidence. In contrast, sub-regions to the cen-

tre and south exhibit levels of relatively lower incidence.

The main hypothesis for these results could be occur-

rence of other factors such as indoor pulverization,

proximity to water basins, etc. However, the absence of

this information has prevented the inclusion of these

variables in the analysis. Furthermore, as malaria has a

certain period of latency it would ideally be not to

Table 4 Posterior estimates of intercept a, environmental

regression coefficients b, of spatial σ2

temporal σ2

δvariances obtained by fitting model B

(Table 3), including 95% credible intervals.

VariableMean

Intercept (a)

-4.248

Rainfall (mm)

-4.30E-

θand spatio-

95% CIP-value

-4.389, -4.124

-9.54E04, 1.01E-

05

None

.059

04

Minimal Temperature (°C)

-.005 -.01, 1.11E–04

2.85E-04

Maximum Temperature (°C)

-.001

.0026.39E-04, .004

.006

Relative Humidity (%)

.007

.006

.007

5.24E-04

3.686

.2352

(11-16.4)

(17-21.1)

.055

.96-.003, .005

(24.5-27)

(28-31)

(32-35)

-.006, .003.55

.001

< .001.003, .009

(52-61.56)

(62-72)

(73-83)

.004, .011

.004, .007

.005, .009

-.002 .003

.871, 10.81

.214, .258

< .001

< .001

< .001

.61

None

None

Temperature variation

Spatial variation (σ2

Spatio-temporal variation

(σ2

θ)

δ)

Zacarias and Andersson Malaria Journal 2011, 10:189

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include the information about for example present

indoor pulverization, but this activity in the past. On the

other hand, it is not observed a single temporal gradient

of malaria relative risk, with some areas showing a

decrease and others exhibit a relative increase. Further-

more, the quantification of relative amount of spatial

risk pattern has helped highlighting districts with low

and high proportions of malaria incidence at a given

time period [11]. In addition, this study may also contri-

bute to the evidence of the importance of spatial and

temporal smoothing of random effects in mapping

malaria [9,11,21-23].

This study showed that the combination of the

monthly maximum temperature in the range 28 to 35°C

and relative humidity in the range 54.5% to 83% pro-

vided suitable condition for malaria transmission. The

negative association attained by maximum temperature

in the range of 24 to 27°C to malaria incidence, could

indicate a need of warmer temperatures for malaria

transmission [11]. The performance of rainfall in the

analysis could be influenced by the presence of humidity

covariate. High levels of humidity is generally observed

when temperature and rainfall are also high, thus lead-

ing to suitable conditions of parasite development due

to available breeding sites and survival of mosquitoes

population [24].

The mapping of averaged smoothed incidence malaria

risk for each month and ten years period allows a

visually display for months of initial and peak transmis-

sion. See Additional files (Additional Files 3 and 4). This

may provide information on the length of transmission

based on the predicted relationship with the included

covariates. Although this study does not present seaso-

nal analysis of malaria incidence variation as in [11], the

monthly variation illustrates some seasonal pattern in

months May-July (usually considered part of winter per-

iod in Mozambique), where the warmer temperatures

may have induced the reduction of the die-back mosqui-

toes and parasite levels, increasing substantially their

availability in the following months. Nevertheless, the

climate remains the main limiting factor of malaria

intensity controlling transmission at both spatial and

temporal dimension [25,26].

In conclusion, the models applied in this study

adjusted for unobserved spatial and temporal variation

on risk factors, while allowing for inter-monthly and

inter-annual variation in malaria incidence to be influ-

enced by environmental conditions. Nevertheless, the

variation on incidence malaria risks could also be

affected by other factors not considered in the analysis.

These results may be useful for developing of climate

based malaria surveillance systems in Mozambique

which can help bring a better management and imple-

mentation of nation-wide malaria control programmes,

by guiding public and private policies towards reducing

malaria incidence in Maputo province. Variation from

normal monthly minimal temperature and rainfall pat-

terns in this study, showed their limited use for predict-

ing malaria incidence in Maputo province.

Additional material

Additional file 1: Standard mortality rate maps for months January

to July.

Additional file 2: Standard mortality rate maps for months August

to December.

Additional file 3: Relative risk for months January to June.

Additional file 4: Relative risk for months July to December.

Abbreviations

MCMC: Markov Chain Monte Carlo; DIC: Deviance Information Criteria; NMCP:

National Malaria Control Program; INAM: Mozambique National Meteorology

Institute; RR: Relative risk; UEM: Universidade Eduardo Mondlane; SIDA:

Swedish International Development Cooperation Agency; CI: Confidence

Interval; BES: Weekly Epidemiological Bulletin; CI: Credible Interval; AR(1): First

Autoregressive Process; SE: Standard Error.

Acknowledgements

Thanks to SIDA and UEM - Project for Global Research in Mathematics,

Statistics and Informatics for supporting this research.

Author details

1Department of Mathematics and Informatics (DMI), Eduardo Mondlane

University, Maputo, Mozambique.2Department of Computer and System

Sciences (DSV), Stockholm University, Stockholm, Sweden.3Department of

Mathematics, Division of Mathematical Statistics, Stockholm University,

Stockholm, Sweden.

Authors’ contributions

MA was responsible for analyses, interpretation of data and results and

manuscript’s revision. OPZ was responsible for conception and study design,

analysis, data interpretation and modelling and manuscript’s drafting and

revision. The authors read and approved the manuscript.

Competing interests

The authors declare that they have no competing interests.

Received: 24 November 2010 Accepted: 13 July 2011

Published: 13 July 2011

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doi:10.1186/1475-2875-10-189

Cite this article as: Zacarias and Andersson: Spatial and temporal

patterns of malaria incidence in Mozambique. Malaria Journal 2011

10:189.

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