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Application of the backstepping method to the prediction of increase or decrease of infected population.

Kuniya T, Sano H - Theor Biol Med Model (2016)

Bottom Line: In mathematical epidemiology, age-structured epidemic models have usually been formulated as the boundary-value problems of the partial differential equations.Under an assumption that the period of infectiousness is same for all infected individuals (that is, the recovery rate is given by the Dirac delta function multiplied by a sufficiently large positive constant), the prediction method is simplified to the comparison of the numbers of reported cases at the current and previous time steps.It was higher than that of the ARIMA models with different orders of the autoregressive part, differencing and moving-average process.

View Article: PubMed Central - PubMed

Affiliation: Department of Applied Mathematics, Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe, 657-8501, Japan. toshikazu.kuniya@gmail.com.

ABSTRACT

Background: In mathematical epidemiology, age-structured epidemic models have usually been formulated as the boundary-value problems of the partial differential equations. On the other hand, in engineering, the backstepping method has recently been developed and widely studied by many authors.

Methods: Using the backstepping method, we obtained a boundary feedback control which plays the role of the threshold criteria for the prediction of increase or decrease of newly infected population. Under an assumption that the period of infectiousness is same for all infected individuals (that is, the recovery rate is given by the Dirac delta function multiplied by a sufficiently large positive constant), the prediction method is simplified to the comparison of the numbers of reported cases at the current and previous time steps.

Results: Our prediction method was applied to the reported cases per sentinel of influenza in Japan from 2006 to 2015 and its accuracy was 0.81 (404 correct predictions to the total 500 predictions). It was higher than that of the ARIMA models with different orders of the autoregressive part, differencing and moving-average process. In addition, a proposed method for the estimation of the number of reported cases, which is consistent with our prediction method, was better than that of the best-fitted ARIMA model ARIMA(1,1,0) in the sense of mean square error.

Conclusions: Our prediction method based on the backstepping method can be simplified to the comparison of the numbers of reported cases of the current and previous time steps. In spite of its simplicity, it can provide a good prediction for the spread of influenza in Japan.

No MeSH data available.


Related in: MedlinePlus

The time series of the actual number of reported cases per sentinel of influenza in Japan (blue) and the values estimated by our method (green) and ARIMA(1,1,0) (red) for 522 weeks from the first week of 2006 to the last week of 2015
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Fig4: The time series of the actual number of reported cases per sentinel of influenza in Japan (blue) and the values estimated by our method (green) and ARIMA(1,1,0) (red) for 522 weeks from the first week of 2006 to the last week of 2015

Mentions: where k>0 is a fitting parameter. It is easy to see that (14) is consistent with our prediction method (that is, if I(t,0)>U(t), then I(t+1,0)>I(t,0) and if I(t,0)<U(t), then I(t+1,0)<I(t,0)). Using the actual data from 2005 to 2015, we perform an ongoing estimation from the first week of 2006 to the last week of 2015. To minimize the mean square error between the actual number of reported cases and our estimated values, k is chosen to be 0.6 (see Fig. 3). In this case, the mean square error of our estimation is 6.17457371, while that of the best-fitted ARIMA model ARIMA(1,1,0) is 9.469997. The estimation result is shown in Fig. 4. In Fig. 4, it is seen that although three curves take close values, some values estimated by ARIMA(1,1,0) are negative.Fig. 3


Application of the backstepping method to the prediction of increase or decrease of infected population.

Kuniya T, Sano H - Theor Biol Med Model (2016)

The time series of the actual number of reported cases per sentinel of influenza in Japan (blue) and the values estimated by our method (green) and ARIMA(1,1,0) (red) for 522 weeks from the first week of 2006 to the last week of 2015
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4862096&req=5

Fig4: The time series of the actual number of reported cases per sentinel of influenza in Japan (blue) and the values estimated by our method (green) and ARIMA(1,1,0) (red) for 522 weeks from the first week of 2006 to the last week of 2015
Mentions: where k>0 is a fitting parameter. It is easy to see that (14) is consistent with our prediction method (that is, if I(t,0)>U(t), then I(t+1,0)>I(t,0) and if I(t,0)<U(t), then I(t+1,0)<I(t,0)). Using the actual data from 2005 to 2015, we perform an ongoing estimation from the first week of 2006 to the last week of 2015. To minimize the mean square error between the actual number of reported cases and our estimated values, k is chosen to be 0.6 (see Fig. 3). In this case, the mean square error of our estimation is 6.17457371, while that of the best-fitted ARIMA model ARIMA(1,1,0) is 9.469997. The estimation result is shown in Fig. 4. In Fig. 4, it is seen that although three curves take close values, some values estimated by ARIMA(1,1,0) are negative.Fig. 3

Bottom Line: In mathematical epidemiology, age-structured epidemic models have usually been formulated as the boundary-value problems of the partial differential equations.Under an assumption that the period of infectiousness is same for all infected individuals (that is, the recovery rate is given by the Dirac delta function multiplied by a sufficiently large positive constant), the prediction method is simplified to the comparison of the numbers of reported cases at the current and previous time steps.It was higher than that of the ARIMA models with different orders of the autoregressive part, differencing and moving-average process.

View Article: PubMed Central - PubMed

Affiliation: Department of Applied Mathematics, Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe, 657-8501, Japan. toshikazu.kuniya@gmail.com.

ABSTRACT

Background: In mathematical epidemiology, age-structured epidemic models have usually been formulated as the boundary-value problems of the partial differential equations. On the other hand, in engineering, the backstepping method has recently been developed and widely studied by many authors.

Methods: Using the backstepping method, we obtained a boundary feedback control which plays the role of the threshold criteria for the prediction of increase or decrease of newly infected population. Under an assumption that the period of infectiousness is same for all infected individuals (that is, the recovery rate is given by the Dirac delta function multiplied by a sufficiently large positive constant), the prediction method is simplified to the comparison of the numbers of reported cases at the current and previous time steps.

Results: Our prediction method was applied to the reported cases per sentinel of influenza in Japan from 2006 to 2015 and its accuracy was 0.81 (404 correct predictions to the total 500 predictions). It was higher than that of the ARIMA models with different orders of the autoregressive part, differencing and moving-average process. In addition, a proposed method for the estimation of the number of reported cases, which is consistent with our prediction method, was better than that of the best-fitted ARIMA model ARIMA(1,1,0) in the sense of mean square error.

Conclusions: Our prediction method based on the backstepping method can be simplified to the comparison of the numbers of reported cases of the current and previous time steps. In spite of its simplicity, it can provide a good prediction for the spread of influenza in Japan.

No MeSH data available.


Related in: MedlinePlus