Seasonal Time Series Models for Forecasting Pertussis Endemic with Holt-Winter's Exponential Smoothing
DOI:
https://doi.org/10.21580/wjit.2026.8.1.16856Keywords:
Pertussis , Time Series Forecasting , MAPE , Disease Surveillance, Holt–Winters Exponential SmoothingAbstract
Accurate forecasting of pertussis cases can support disease surveillance and public health planning. This study evaluates the application of Holt–Winters exponential smoothing to forecast weekly pertussis cases in the United States. The study uses weekly case data reported by the Centers for Disease Control and Prevention (CDC) and the Florida Department of Health, covering the period from 2008 to 2012, with four additional observations from the final weeks of 2007 included as initial data. Two Holt–Winters configurations were evaluated using seasonal periods of 4 and 13 weeks. The dataset was divided into training and testing sets at a ratio of 80:20, and forecasting accuracy was assessed using the Mean Absolute Percentage Error (MAPE). The reported results show that the 4-week configuration achieved a MAPE of 34.7898%, whereas the 13-week configuration achieved a MAPE of 40.7340%. Thus, the 4-week configuration produced a lower MAPE than the 13-week configuration for the data evaluated in this study. However, the results should be interpreted within the scope of the selected dataset and seasonal configurations. Further evaluation using alternative seasonal periods, clearly specified testing procedures, and additional datasets is necessary to determine the robustness and generalizability of the forecasting performance.
Downloads
References
Bartolomei, S. M., & Sweet, A. L. (1989). A note on a comparison of exponential smoothing methods for forecasting seasonal series. International Journal of Forecasting, 5(1). https://doi.org/10.1016/0169-2070(89)90068-X
Chatfield, C., & Yar, M. (1988). Holt-Winters Forecasting: Some Practical Issues. The Statistician, 37(2). https://doi.org/10.2307/2348687
Chowell, G., & Skums, P. (2024). Investigating and forecasting infectious disease dynamics using epidemiological and molecular surveillance data. In Physics of Life Reviews (Vol. 51). https://doi.org/10.1016/j.plrev.2024.10.011
De Greeff, S. C., Dekkers, A. L. M., Teunis, P., Rahamat-Langendoen, J. C., Mooi, F. R., & De Melker, H. E. (2009). Seasonal patterns in time series of pertussis. Epidemiology and Infection, 137(10). https://doi.org/10.1017/S0950268809002489
Fitria, J. D., Karohmah, N., & Sunarmi. (2017). Peramalan Jumlah Pasien DBD di Rsud Dr. Soeselo Slawi dengan Metode Dekomposisi dan Triple Exponential Smoothing Winter’s. Seminar Nasional Pendidikan, Sains Dan Teknologi.
Gabutti, G., & Rota, M. C. (2012). Pertussis: A review of disease epidemiology worldwide and in Italy. In International Journal of Environmental Research and Public Health (Vol. 9, Number 12). https://doi.org/10.3390/ijerph9124626
Gardner, E. S. (2006). Exponential smoothing: The state of the art-Part II. International Journal of Forecasting, 22(4). https://doi.org/10.1016/j.ijforecast.2006.03.005
Hand, D. J. (2009). Forecasting with Exponential Smoothing: The State Space Approach by Rob J. Hyndman, Anne B. Koehler, J. Keith Ord, Ralph D. Snyder. International Statistical Review, 77(2). https://doi.org/10.1111/j.1751-5823.2009.00085_17.x
Havers, F. P., Moro, P. L., Hariri, S., & Skoff, T. (2015). Centers for Disease Control and Prevention. “Pertussis” from Epidemiology and Prevention of Vaccine-Preventable Diseases. Washington D.C. Public Health Foundation, 2015., 13th Editi.
Holt, C. C. (2004). Forecasting seasonals and trends by exponentially weighted moving averages. International Journal of Forecasting, 20(1). https://doi.org/10.1016/j.ijforecast.2003.09.015
Hyndman, R.J., & Athanasopoulos, G. (2015). Forecasting: Principles and Practice (3rd ed). OTexts: Melbourne, Australia. OTexts.Com/Fpp3.
Nann, D., Walker, M., Frauenfeld, L., Ferenci, T., & Sulyok, M. (2021). Forecasting the future number of pertussis cases using data from Google Trends. Heliyon, 7(11). https://doi.org/10.1016/j.heliyon.2021.e08386
Wang, Y., Xu, C., Wang, Z., Zhang, S., Zhu, Y., & Yuan, J. (2018). Time series modeling of pertussis incidence in China from 2004 to 2018 with a novel wavelet based SARIMA-NAR hybrid model. PLoS ONE, 13(12). https://doi.org/10.1371/journal.pone.0208404
Winters, P. R. (1960). Forecasting Sales by Exponentially Weighted Moving Averages. Management Science, 6(3). https://doi.org/10.1287/mnsc.6.3.324
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Walisongo Journal of Information Technology
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
The copyright of the received article shall be assigned to the journal as the publisher of the journal. The intended copyright includes the right to publish the article in various forms (including reprints). The journal maintains the publishing rights to the published articles. Authors are allowed to use their articles for any legal purposes deemed necessary without written permission from the journal with an acknowledgment of initial publication to this journal.
Licensing
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
