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A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

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

Toshikazu Kuniya¹, Hideki Sano²

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

Theoretical Biology & Medical Modelling

|May 12, 2016

Summary

A new prediction method using the backstepping method accurately forecasts influenza spread by comparing current and past case numbers. This approach offers a simple yet effective tool for epidemiological prediction.

Keywords:

ARIMA Age structure Backstepping method Influenza Prediction

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Area of Science:

Mathematical Epidemiology
Control Theory
Time Series Analysis

Background:

Traditional age-structured epidemic models often use partial differential equations.
The backstepping method, a control engineering technique, has gained recent attention.

Purpose of the Study:

To apply the backstepping method for predicting infectious disease dynamics.
To develop a simplified prediction model for influenza spread.

Main Methods:

Developed a boundary feedback control using the backstepping method.
Simplified the prediction to comparing current and previous reported case numbers.
Assumed a constant infectious period for all individuals.

Main Results:

Achieved 0.81 accuracy in predicting influenza cases in Japan (2006-2015).
Outperformed various Autoregressive Integrated Moving Average (ARIMA) models in prediction accuracy.
A novel estimation method for reported cases showed lower mean square error than the best-fitted ARIMA model.

Conclusions:

The backstepping method provides a simple yet effective influenza prediction tool.
Comparing current and past case numbers offers a robust prediction strategy.
This method demonstrates strong potential for real-world epidemiological forecasting.