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<p>This study investigates the transmission dynamics of Monkeypox disease using a Harmonic neural network (HNN) framework optimized through stochastic gradient descent with momentum (SGDM). The proposed HNN-SGDM approach is applied to a nonlinear Monkeypox model consisting of nine coupled differential equations describing the interactions between human and rodent populations. HNN are employed because traditional non-oscillatory activation functions often struggle to capture the periodic and complex dynamics of disease transmission, whereas harmonic activation functions efficiently approximate such oscillatory patterns. SGDM is chosen to improve convergence and optimization stability in high-dimensional, non-convex search spaces. The proposed solver achieves high precision, with absolute errors ranging from <InlineEquation ID="IEq1"><EquationSource Format="TEX">\(10^{-7}\)</EquationSource></InlineEquation> to <InlineEquation ID="IEq2"><EquationSource Format="TEX">\(10^{-10}\)</EquationSource></InlineEquation>, confirming its numerical stability and convergence. The robustness and reliability of HNN-SGDM framework are further validated through statistical performance measures, including mean absolute error, root mean square error, and Theil’s inequality coefficient. Graphical analyses, including weight distributions, box plots, histograms, and loss curves, further validate the model’s performance. This approach highlights the effectiveness of deep learning in epidemiological modeling and provides a methodology extendable to other infectious disease frameworks.</p>

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A deep learning approach for solving a fractional order Monkeypox transmission model using a harmonic neural network optimized with SGDM

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月26日

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  • Nimra Shoket,
  • Abdul Mannan,
  • Jamshaid Ul Rahman,
  • Ebraheem Alzahrani,
  • Osman Abubakar Fiidow

摘要

This study investigates the transmission dynamics of Monkeypox disease using a Harmonic neural network (HNN) framework optimized through stochastic gradient descent with momentum (SGDM). The proposed HNN-SGDM approach is applied to a nonlinear Monkeypox model consisting of nine coupled differential equations describing the interactions between human and rodent populations. HNN are employed because traditional non-oscillatory activation functions often struggle to capture the periodic and complex dynamics of disease transmission, whereas harmonic activation functions efficiently approximate such oscillatory patterns. SGDM is chosen to improve convergence and optimization stability in high-dimensional, non-convex search spaces. The proposed solver achieves high precision, with absolute errors ranging from \(10^{-7}\) to \(10^{-10}\), confirming its numerical stability and convergence. The robustness and reliability of HNN-SGDM framework are further validated through statistical performance measures, including mean absolute error, root mean square error, and Theil’s inequality coefficient. Graphical analyses, including weight distributions, box plots, histograms, and loss curves, further validate the model’s performance. This approach highlights the effectiveness of deep learning in epidemiological modeling and provides a methodology extendable to other infectious disease frameworks.