PREDICTING THE TRANSMISSION DYNAMICS OF TUBERCULOSIS VIA CAPUTO FRACTIONAL ORDER MODEL WITH NEURAL NETWOR

Document Type : Regular research papers

Abstract

 Abstract. This study presents the development of a hybrid Fractional Order
Dierential Equation (FODE) and Articial Neural Network (ANN) model designed to predict the dynamics of Tuberculosis (TB) in Nigeria. The analysis
utilized data sourced from the World Health Organization (WHO) TB Database and the Nigeria category, spanning the years 2010 to 2020. The Caputo
derivative was used to formulate the fractional tuberculosis model which was
enhanced with an ANN framework. The derived FODEs were discretized using
the Gr¨unwald-Letnikov method for parameter estimation and numerical simulation of the TB data in MATLAB, employing varying memory values for the
fractional-order model parameter 0 < α ≤ 1. To enhance predictive accuracy,
we integrate an Articial Neural Network (ANN) with the FDE model, leveraging machine learning techniques for parameter estimation and forecasting.
The ANN is trained using real-world TB data, employing the sigmoid function
to represent time-dependent transmission rates. Our results demonstrate that
the fractional-order model provides a more exible and accurate representation of TB dynamics compared to classical integer-order models. The proposed
hybrid approach eectively captures disease trends, making it a valuable tool
for epidemiological analysis and public health decision-making. 

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