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Comparative Study
. 2013 May 1;8(5):e63116.
doi: 10.1371/journal.pone.0063116. Print 2013.

Comparative Study of Four Time Series Methods in Forecasting Typhoid Fever Incidence in China

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Free PMC article
Comparative Study

Comparative Study of Four Time Series Methods in Forecasting Typhoid Fever Incidence in China

Xingyu Zhang et al. PLoS One. .
Free PMC article

Abstract

Accurate incidence forecasting of infectious disease is critical for early prevention and for better government strategic planning. In this paper, we present a comprehensive study of different forecasting methods based on the monthly incidence of typhoid fever. The seasonal autoregressive integrated moving average (SARIMA) model and three different models inspired by neural networks, namely, back propagation neural networks (BPNN), radial basis function neural networks (RBFNN), and Elman recurrent neural networks (ERNN) were compared. The differences as well as the advantages and disadvantages, among the SARIMA model and the neural networks were summarized and discussed. The data obtained for 2005 to 2009 and for 2010 from the Chinese Center for Disease Control and Prevention were used as modeling and forecasting samples, respectively. The performances were evaluated based on three metrics: mean absolute error (MAE), mean absolute percentage error (MAPE), and mean square error (MSE). The results showed that RBFNN obtained the smallest MAE, MAPE and MSE in both the modeling and forecasting processes. The performances of the four models ranked in descending order were: RBFNN, ERNN, BPNN and the SARIMA model.

Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. Monthly typhoid fever incidence series of Guangxi province in China from 2005 to 2010.
Figure 2
Figure 2. Schematic of BPNN.
(Note: xi is the ith sample of the input layer, ω ij is the connection weight between the ith input node and the jth node of the hidden layer, f is the activation function of the hidden layer, ω j is the connection weight between the jth node to the output node, O is the output of the network.)
Figure 3
Figure 3. Schematic of RBFNN.
(Note: xi is the ith sample of the input layer, ψ is the RBF function of the hidden layer, ω j is the connection weight between the jth node to the output node, O is the output of the network.)
Figure 4
Figure 4. Schematic of ERNN.
(Note: u(k−1) and y(k) are the input and output of the network, respectively, at a discrete time k; xc(k) and x(k) are the nodes of the context and the hidden layers, respectively; and formula image,formula image, and formula image are the weight matrices for the context-hidden, input-hidden, and the hidden-output layers, respectively.)
Figure 5
Figure 5. Typhoid fever incidence and fitting values for 2010 predicted by the four methods.
Figure 6
Figure 6. Comparison of the performances of the four different models.
Figure 7
Figure 7. Typhoid fever incidence and fitting values predicted by the four methods.
(Note: The data were divided into modeling and forecasting groups with a vertical line; the left is the modeling part, and the right is the forecasting part.)

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References

    1. Cooke FJ, Day M, Wain J, Ward LR, Threlfall EJ (2007) Cases of typhoid fever imported into England, Scotland and Wales (2000–2003). Transactions of the Royal Society of Tropical Medicine and Hygiene 101: 398–404. - PubMed
    1. WHO website. Available: http://www.who.int/csr/don/archive/disease/typhoid_fever/. Accessed 2012 May 6.
    1. Naheed A, Ram PK, Brooks WA, Hossain MA, Parsons MB, et al. (2010) Burden of typhoid and paratyphoid fever in a densely populated urban community, Dhaka,Bangladesh. International Journal of Infectious Diseases 14 Supplement 3e93–e99. - PubMed
    1. Cvjetanovic B, Grab B, Dixon H (1986) Computerized epidemiological model of typhoid fever with age structure and its use in the planning and evaluation of antityphoid immunization and sanitation programmes. Mathematical Modelling 7: 719–744. - PMC - PubMed
    1. Cvjetanovic B, Grab B, Uemura K (1971) Epidemiological model of typhoid fever and its use in the planning and evaluation of antityphoid immunization and sanitation programmes. Bulletin of the World Health Organization 45: 53–75. - PMC - PubMed

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Grant support

The whole study and the paper were financially supported by the National Special Foundation for Health Research of China (grant no. 200802133). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
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