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.
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
E-mail: nahid_bau@yahoo.co.in; Phone: +610430504183
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dengue fever may have been occurring sporadically in Bangladesh from 1964 to 1999[39] . 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.
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 Dengue Bulletin – Volume 32, 2008
Materials and methods Study area Dhaka is the capital and principal city of Bangladesh located at 23° 42’ 0" N, 90° 22’ 30
Forecasting dengue incidence in Dhaka, Bangladesh: A time series analysis
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 nonstationary 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 nonseasonal 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 3500 3000 2500 2000 1500 1000 500 0 MAY 2001 MAY 2002 MAY 2003 MAY 2004 MAY 2000 SEP 2000 JAN 2001 SEP 2001 JAN 2002 SEP 2002 SEP 2003 SEP 2004 MAY 2005 SEP 2005 MAY 2006 SEP 2006 MAY 2007 SEP 2007 JAN 2003 JAN 2004 JAN 2005 JAN 2006 JAN 2000 JAN 2007
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Table 1: MAPE and normalized BIC of Time Series Models Models SARIMA(2,1,1)(1,1,0)12 SARIMA(2,1,0)(1,1,0)12 SARIMA(1,1,1)(1,1,0)12 SARIMA(0,1,0)(1,1,0)12 SARIMA(1,1,0)(1,1,0)12 SARIMA(1,1,1)(1,1,1)12 SARIMA(1,1,1)(2,1,0)12 SARIMA(1,0,1)(1,1,1)12 SARIMA(1,0,1)(1,1,0)12 SARIMA(1,0,0)(1,1,1)12 MAPE 1026.050 766.310 945.640 805.376 791.408 947.663 975.253 600.730 717.614 595.346 Normalized BIC 12.072 12.215 12.052 12.236 12.269 12.059 12.071 11.952 11.933 11.918
Table 2: Model parameters of SARIMA (1,0,0)(1,1,1)12 Variable AR (Lag 1) AR, Seasonal (Lag 1) Seasonal Difference MA, Seasonal (Lag 1) β 0.385 -0.587 1.000 0.405 0.151 0.009 SE 0.106 0.109 p-value 0.000 0.000
Figure 2a: ACF of transformed series with seasonal difference (1, period 12)
Coefficient Upper Confidence Limit Lower Confidence Limit
ACF
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Forecasting dengue incidence in Dhaka, Bangladesh: A time series analysis
Figure 2b: PACF of transformed series with seasonal difference (1, period 12)
Coefficient Upper Confidence Limit Lower Confidence Limit
Partial ACF
Lag Number
Figure 2c: ACF of transformed series with non-seasonal difference (1) and seasonal difference (1, period 12) Coefficient Upper Confidence Limit Lower Confidence Limit
ACF
Lag Number
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Figure 2d: PACF of transformed series with non-seasonal difference (1) and seasonal difference (1, period 12) Coefficient Upper Confidence Limit Lower Confidence Limit
Partial ACF
Lag Number
Figure 3: Dengue incidence: Observed values and predicted values of SARIMA (1,0,0)(1,1,1)12 3500
3000
2500
Observed 2000
Predicted
1500
1000
500
0 APR 2000 OCT 2000 APR 2001 OCT 2001 JAN 2000 JUL 2000 APR 2002 OCT 2002 JAN 2001 JUL 2001 OCT 2003 APR 2003 JAN 2002 JUL 2002 APR 2004 OCT 2004 JAN 2003 JUL 2003 OCT 2005 APR 2005 JAN 2004 JUL 2004 APR 2006 OCT 2006 JAN 2005 JUL 2005 APR 2007 OCT 2007 JAN 2006 JUL 2006 JAN 2007 JUL 2007
-500
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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 500
400
Predicted 300
200
100
Observed
0 NOV 2006 AUG 2007 MAR 2007 JAN 2007 APR 2007 MAY 2007 OCT 2006 OCT 2007 DEC 2006 JUN 2007 JUL 2007 SEP 2006 FEB 2007 SEP 2007
-100
Figure 5: Forecast of dengue incidence from November 2007 to December 2008 by SARIMA (1,0,0)(1,1,1)12 800 700 600 500 400 300 200 100 0 JUL 2008 AUG 2008 NOV 2007 -100 NOV 2008 DEC 2007 MAR 2008 MAY 2008 OCT 2008 DEC 2008 JAN 2008 JUN 2008 FEB 2008 APR 2008 SEP 2008
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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 wellpractised 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.
References [1] Rigau-Perez JG, Clark GC, Gubler DJ, Reiter P , Sanders EJ, Vorndam AV. Dengue and dengue haemorrhagic fever. Lancet. 1998 Sept 19; 352(9132): 971-977. [2] Nimmannitya S. Clinical manifestations of dengue and dengue haemorrhagic fever: monograph on dengue and dengue haemorrhagic fever . WHO Regional Publication SEARO No. 22. New Delhi: World Health Organization, Regional Office for South-East Asia, 1983; pp. 48-53. [3] Aziz MA, Graham RR, Gregg MB. “Dacca fever”-an outbreak of dengue. Pak J Med Res. 1967; 6: 83-92. [4] Gaidamovich SY, Siddiqi SM, Haq F, Klisenko GA, Melnikova EE, Obukhova VR. Serological evidence of dengue fever in the Bangladesh Republic. Acta Virol. 1980; 24: 153. [5] Islam MN, Khan AQ, Khan AN. Viral disease in Bangladesh: procedings of an International Seminer on viral disease in South- East- Asian and Western Pasific, Feb. 8-12 Canbera, Australia, Washing DC, USA. Washington DC: Academic Press, 1982. [6] Khan AM, Ahamed TU. Dengue status in Bangladesh. Dengue News. 1986; 12-11.
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[7] Amin MMM, Hussain AMZ, Murshed M, Chowdury IA, Banu D. Sero-diagnosis of dengue infections by haemagglutination inhibition (HI) in suspected cases in Chittagong, Bangladesh. Dengue Bull. 1999; 23: 34–38. [8] Alam MN. Dengue and dengue haemorrhagic fever in Bangladesh. Orion Med J . 2000; 6: 7-10. [9] Hossain MA, Khatun M, Arjumand F, Nisaluk A, Breiman RF. Serologic evidence of dengue infection before onset of epidemic, Bangladesh. Emerg Infect Dis. 2003 Nov; 9: 1411-1414. [10] Rahman M, Rahman K, Siddque A K, Shoma S, Kamal AHM, Ali KS, Nisaluk A, Breiman RF. First Outbreak of Dengue Hemorrhagic Fever, Bangladesh. Emerg Infect Dis. 2002 July; 8: 738-740. [11] Aziz MM, Hasan KH, Hasanat MA, Siddiqui MA, Salimullah M, Chowdhury AK, Ahmed M, Alam MN, Hassan MS. Predominance of the DEN-3 genotype during the recent dengue outbreak in Bangladesh. Southeast Asian J Trop Med Public Health. 2002; 33: 42-48. [12] Bowie C, Prothero D. Finding causes of seasonal diseases using time series analysis. Int J Epidemiol. 1981; 10: 87–92. [13] Allard R. Use of time-series analysis in infectious disease surveillance. Bull World Health Organ. 1998; 76: 327–333. [14] Helfenstein U. Box-Jenkins modelling of some viral infectious diseases. Stat Med. 1986; 5: 37-47. [15] Catalano R, Serxner S. Time series designs of potential interest to epidemiologists. Am J Epidemiol. 1987; 126: 724-731. [16] Helfenstein U. Box-Jenkins modelling in medical research. Stat Methods Med Res. 1996; 5:3-22.
[17] Helfenstein U. The use of transfer function models, intervention analysis and related time series methods in epidemiology. Int J Epidemiol. 1991; 20: 808–815. [18] Abraham B, Ledolter J. Statistical Methods for Forecasting. New York: Wiley, 1983. pp. 225229, 336-355. [19] Wongkoon S, Pollar M, Jaroensutasinee M, Jaroensutasinee K. Predicting DHF incidence in Northern Thailand using time series analysis technique. Proceedings of World Academy of Science, Engineering and Technology. 2007; 26: 216-220. [20] Naish S, Hu W, Nicholls N, Mackenzie JS, McMichael AJ, Dale P, Tong S. Weather variability, tides, and barmah forest virus disease in the Gladstone region, Australia. Environ Health Perspect. 2006; 114: 678-683. [21] Hu W, Nicholls N, Lindsay M, Dale P, McMichael AJ, Mackenzie JS, Tong S. Development of a predictive model for Ross River Virus Disease in Brisbane, Australia. Am J Trop Med Hyg. 2004; 71: 129-137. [22] Promprou S, Jaroensutasinee M, Jaroensutasinee K. Forecasting Dengue Haemorrhagic Fever Cases in Southern Thailand using ARIMA Models. Dengue Bull. 2006; 30: 99-106. [23] World Gazetteer. (Web site) http://worldgazetteer.com/ , 2006. [24] Directorate General of Health Services. Dengue register, Disease Control Directorate. Dhaka: DGHS, 2000. [25] Makridakis S, Wheelwright SC, Hyndman RJ. Forecasting: methods and applications. 3rd ed. New York: Wiley, 1998. [26] Schwarz G. Estimating the dimension of a model. Ann Statist. 1978; 6: 461-464. [27] Brockwell P , Davis R. Introduction to time series and forecasting. New York: Springer, 2002.
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