DengueWHO_MdChoudhury.pdf

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Forecasting dengue incidence in Dhaka, Bangladesh: A time series analysis
Article in Dengue Bulletin · December 2008
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Dengue Bulletin – Volume 32, 2008 29
Forecasting dengue incidence in Dhaka, Bangladesh:
A time series analysis
M.A.H. Zamil Choudhurya,b#
, Shahera Banub
, M. Amirul Islamc,d
a
International Centre for Diarrhoeal Disease Research, Bangladesh (ICDDR,B), Mohakhali,
Dhaka-1212, Bangladesh
b
Department of Microbiology and Hygiene, Bangladesh Agricultural University,
Mymensingh 2202, Bangladesh
c
Department of Agricultural Statistics, Bangladesh Agricultural University, Mymensingh 2202, Bangladesh
d
Southampton Statistical Sciences Research Institute, University of Southampton, UK
Abstract
This article attempts to model the monthly number of dengue fever (DF) cases in Dhaka, Bangladesh,
and forecast the dengue incidence using time series analysis. Seasonal Autoregressive Integrated Moving
Average (SARIMA) models have been developed on the monthly data collected from January 2000 to
October 2007 and validated using the data from September 2006 to October 2007. The results
showed that the predicted values were consistent with the upturns and downturns of the observed
series. The SARIMA (1,0,0)(1,1,1)12
model has been found as the most suitable model with least
Normalized Bayesian Information Criteria (BIC) of 11.918 and Mean Absolute Percent Error (MAPE) of
595.346. The model was further validated by Ljung-Box test (Q18=15.266 and p>.10) with no
significant autocorrelation between residuals at different lag times. Finally, a forecast for the period
November 2007 to December 2008 was made, which showed a pick in the incidence of DF during
July 2008, with estimated cases as 689.
Keywords: Dengue; Time series analysis; SARIMA; Disease prediction; Dhaka, Bangladesh.
#
E-mail: nahid_bau@yahoo.co.in; Phone: +610430504183
Introduction
Dengue is one of the most important emerging
viral diseases of major public health concern
in Bangladesh. The disease is transmitted
through the bite of the Aedes aegypti and Ae.
albopictus mosquitoes[1]
. It causes a broad
spectrum of clinical manifestations in humans
ranging from the acute febrile illness, dengue
fever (DF), to the life-threatening dengue
haemorrhagic fever/dengue shock syndrome
(DHF/DSS)[2]
.
Dengue was first reported as “Dacca fever”
in Bangladesh in 1964 by Aziz and his
colleagues[3]
. Subsequent reports suggested that

30 Dengue Bulletin – Volume 32, 2008
dengue fever may have been occurring
sporadically in Bangladesh from 1964 to 1999[3-
9]
. The first epidemic of dengue was reported
in the capital city, Dhaka in the year 2000[10,11]
.
Since then the disease has shown an annual
occurrence in all major cities of the country.
During January 2000–December 2007,
Bangladesh recorded a total of 22 245 cases
and 233 deaths (1.04%). Of these, Dhaka
accounted for 20 115 cases and 181 deaths
(0.9%).
In the absence of a vaccine and specific
treatment available for dengue, vector control
remains the only option. Early warning about
the disease based on forecasting, therefore,
becomes crucial for the prevention and control
of dengue in Bangladesh. The time series
analyses methodology has been increasingly
used in the field of epidemiological research
on infectious diseases, particularly in the
assessment of health services[12-16]
. In health
science research, Autoregressive Integrated
Moving Average (ARIMA) models[12-18]
as well
as Seasonal Autoregressive Integrated Moving
Average (SARIMA)[19-20]
models are useful tools
for analysing time series data containing ordinary
or seasonal trends to develop a predictive
forecasting model. There have been efforts in
forecasting dengue incidence in different parts
of the world using both ARIMA[21,22]
and
SARIMA[19]
modelling. This study is aimed at
developing univarite time series models to
forecast the monthly dengue incidence in
Dhaka based on reported monthly cases
available from 2000–2007. This forecasting
offers the potential for improved and consistent
planning of public health interventions.
Materials and methods
Study area
Dhaka is the capital and principal city of
Bangladesh located at 23° 42’ 0" N, 90° 22’
30" E, covering an area of 815.85 km2
(315 sq
miles). According to the World Gazetteer
(2006), the population in the Dhaka region was
11 million and the density was 14 608/km²
(37 834.5/sq mile) making it the largest city in
Bangladesh and the eleventh most populous
city in the world[23]
. The Dhaka region was
chosen as the study area because of its
relatively high incidence of DF between 2000
and 2007 (average annual incidence: 2515.75
cases).
Data collection
We obtained computerized data sets of
notifications of monthly DF cases in the Dhaka
region for the period 1 January 2000 through
31 October 2007 from the Directorate-General
of Health Services, Mohakhali, Dhaka-1212[24]
.
It may be noted that the Directorate-General
of Health Services collects information on
dengue cases separately as DF, DHF and DSS
but clubs this data as data for DF only.
Data analysis
A SARIMA (p,d,q)(P
,D,Q)S
model[25]
was fitted,
where p is the order of autoregression, d is
the order of integration, q is the order of moving
average, P is the order of seasonal
autoregression, D is the order of seasonal
integration, Q is the order of seasonal moving
average and s is the length of seasonal period.
The analyses were performed using SPSS 17
software. The stationarity of the series was
made by means of seasonal and non-seasonal
differencing[25]
.Then the order of autoregression
and moving average were identified using
autocorrelation function (ACF) and partial
autocorrelation function (PACF) of the
differenced series. A model was fitted with a
training set of data from January 2000 to
October 2007 and the fitted model was used
to predict values for a validation period (from

September 2006 to October 2007) to evaluate
the time series model. Most suitable models
were selected on the basis of their ability of
reliable prediction. Two measures, namely,
Normalised Bayesian Information Criteria
(BIC)[26]
and Mean Absolute Percent Error
(MAPE)[25]
, were used. Lower values of
Normalised BIC and MAPE were preferable.
Furthermore, Ljung-Box test (portmanteau test)
was performed to test if the residual ACF at
different lag times was significantly different
from zero, where not being different from zero
was expected[27]
. After the best model was
identified, forecast for future values from
November 2007 to December 2008 was made.
Results and discussion
The observed series of DF (January 2000 to
October 2007) shows that the series is non-
stationary and there are seasonal fluctuations
in the dataset (Figure 1). ACF and PACF of one
seasonal differenced series (Figure 2a, Figure
2b) as well as of one seasonal with one non-
seasonal differenced series (Figure 2c, Figure
2d) instigated to explore a set of models based
on the training set of data (January 2000 to
October 2007), which are listed in Table 1.
Among these models, SARIMA(1,0,0)(1,1,1)12
has both lowest normalised BIC (11.918) and
MAPE (595.346) values and appeared to be
the best model. Moreover, the Ljung-Box test
suggested that the ACF of residuals for the
model at different lag times was not significantly
different from zero (Q18=15.266 and p>.10).
All the coefficients of SARIMA (1,0,0)(1,1,1)12
model were significant (Table 2). The model
has been used to predict values from September
2006 to October 2007 (Figures 3 and 4) for
validation. It appeared that the predicted values
could follow the upturn and downturn of the
observed series reasonably well. Finally, Figure
5 represents the forecast values for the period
from November 2007 to December 2008,
which indicates a seasonal pick in July 2008,
with the estimated number of patients as 689
and a sharp decrease from September 2008.
The predicted values as well as the forecast
values show some negative values, which is a
common case with a series with too many zeros
as observed values in the series.
Figure 1: Observed dengue fever from January 2000 to October 2007
0
500
1000
1500
2000
2500
3000
3500
JAN
2000
MAY
2000
SEP
2000
JAN
2001
MAY
2001
SEP
2001
JAN
2002
MAY
2002
SEP
2002
JAN
2003
MAY
2003
SEP
2003
JAN
2004
MAY
2004
SEP
2004
JAN
2005
MAY
2005
SEP
2005
JAN
2006
MAY
2006
SEP
2006
JAN
2007
MAY
2007
SEP
2007

Table 1: MAPE and normalized BIC of Time Series Models
Models MAPE Normalized BIC
SARIMA(2,1,1)(1,1,0)12
1026.050 12.072
SARIMA(2,1,0)(1,1,0)12
766.310 12.215
SARIMA(1,1,1)(1,1,0)12
945.640 12.052
SARIMA(0,1,0)(1,1,0)12
805.376 12.236
SARIMA(1,1,0)(1,1,0)12
791.408 12.269
SARIMA(1,1,1)(1,1,1)12
947.663 12.059
SARIMA(1,1,1)(2,1,0)12
975.253 12.071
SARIMA(1,0,1)(1,1,1)12
600.730 11.952
SARIMA(1,0,1)(1,1,0)12
717.614 11.933
SARIMA(1,0,0)(1,1,1)12
595.346 11.918
Table 2: Model parameters of SARIMA (1,0,0)(1,1,1)12
Variable β
β
β
β
β SE p-value
AR (Lag 1) 0.385 0.106 0.000
AR, Seasonal (Lag 1) -0.587 0.109 0.000
Seasonal Difference 1.000
MA, Seasonal (Lag 1) 0.405 0.151 0.009
Figure 2a: ACF of transformed series with seasonal difference (1, period 12)
Coefficient
Upper Confidence Limit
Lower Confidence Limit
Lag Number
ACF

Figure 2b: PACF of transformed series with seasonal difference (1, period 12)
Coefficient
Lag Number
Partial
ACF
Figure 2c: ACF of transformed series with non-seasonal difference (1) and
seasonal difference (1, period 12)
Coefficient
Lag Number
ACF

Figure 2d: PACF of transformed series with non-seasonal difference (1) and
seasonal difference (1, period 12)
Coefficient
Lag Number
Partial
ACF
Figure 3: Dengue incidence: Observed values and predicted values of SARIMA (1,0,0)(1,1,1)12
-500
0
500
1000
1500
2000
2500
3000
3500
JAN
2000
APR
2000
JUL
2000
OCT
2000
JAN
2001
APR
2001
JUL
2001
OCT
2001
JAN
2002
APR
2002
JUL
2002
OCT
2002
JAN
2003
APR
2003
JUL
2003
OCT
2003
JAN
2004
APR
2004
JUL
2004
OCT
2004
JAN
2005
APR
2005
JUL
2005
OCT
2005
JAN
2006
APR
2006
JUL
2006
OCT
2006
JAN
2007
APR
2007
JUL
2007
OCT
2007
Observed Predicted

Figure 4: Dengue incidence – Observed values and predicted values of SARIMA
(1,0,0)(1,1,1)12
for the period September 2006 to October 2007
-100
0
100
200
300
400
500
SEP
2006
OCT
2006
NOV
2006
DEC
2006
JAN
2007
FEB
2007
MAR
2007
APR
2007
MAY
2007
JUN
2007
JUL
2007
AUG
2007
SEP
2007
OCT
2007
Predicted
Observed
Figure 5: Forecast of dengue incidence from November 2007 to December 2008 by
SARIMA (1,0,0)(1,1,1)12
-100
0
100
200
300
400
500
600
700
800
NOV
2007
DEC
2007
JAN
2008
FEB
2008
MAR
2008
APR
2008
MAY
2008
JUN
2008
JUL
2008
AUG
2008
SEP
2008
OCT
2008
NOV
2008
DEC
2008

Conclusion
The incidence of dengue fever every year in
Bangladesh, especially in Dhaka city, is a
constant threat to the population and a recurring
problem for the health authorities.
Furthermore, all environmental conditions that
can trigger an outbreak are more or less present
in the country. Forecasting a dengue outbreak
can help the authorities to take effective
measures to handle any unexpected situation.
Such an effort is cost-effective considering the
financial constraints of the health sector. The
present study is the first of its kind in
Bangladesh. The SARIMA results revealed that
the number of dengue patients in 2008 will
have a seasonal pick with the highest value as
689 in July, which is concordant with our
previous experience. SARIMA models are well-
practised tools in epidemiological research
which may offer further accuracy in prediction
if some relevant variables[20,21
, for example,
temperature, humidity, rainfall, are considered
during the modelling process. Efforts should
be made in the future to use such additional
information, which was not possible in the
current study due to lack of coordination
between different sources as well as
dissimilarity of area of coverage by different
authorities. Separate modelling approaches for
DF, DHF and DSS would provide better
information to policy-makers and planners.
Relevant data should be made available in a
timely manner, possibly from one service point,
with proper coordination between different
data sources.
Acknowledgements
We thank the Disease Control Directorate,
Directorate-General of Health Services, Dhaka,
Bangladesh, for providing the data of notified
dengue cases between 2000 to 2007. We also
thank Professor Dr Md Alimul Islam for his
suggestions and inspiration. Finally, we would
like to thank the three anonymous reviewers
for their valuable comments on the previous
version of the manuscript.
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