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<p>Artificial Neural Networks (ANNs) have emerged as powerful tools for modeling the highly nonlinear dynamics inherent in epidemiological systems. In particular, the Coronavirus Disease 2019 (COVID-19) pandemic has presented unprecedented challenges due to its multi-wave behavior, variable transmission dynamics, and uncertain external influences. This study introduces a novel computational approach for simulating the generalized COVID-19 epidemic by integrating a Morlet Wavelet Neural Network (MWNN) with a hybrid metaheuristic optimization technique that synergizes Genetic Algorithm (GA) and Adaptive Simulated Annealing (ASA). Motivated by the need to simulate more realistic and adaptable transmission patterns in epidemic modeling, the underlying study incorporates stochastic dynamics and explores three distinct recruitment rate functions: two oscillatory periodic profiles with varying amplitudes and frequencies, and one exponentially decaying non-periodic profile, each reflecting plausible real-world recruitment behaviors. To ensure the theoretical rigor of the model, a comprehensive mathematical analysis is conducted, wherein the existence and uniqueness of solutions are established using the Banach Fixed-Point Theorem through an appropriate contraction mapping, and the positivity of solutions is rigorously verified. The performance of the proposed MWNN-GA–ASA method is thoroughly validated via statistical indicators, including Mean Absolute Error (MAE) and Root Mean Square Error (RMSE), demonstrating excellent accuracy and convergence. Furthermore, comparative analyses against the Non-Standard Finite Difference (NSFD) method are conducted, supported by box plots, Kernel Density Estimates (KDEs), and loss function curves, showcasing superior performance and error consistency. The model’s reliability is further reinforced by the learning of optimal weight vectors and careful tuning of learning rates, batch size, and training epochs, all of which contribute to its robust generalization and precision. The integration of wavelet theory, deep learning, and hybrid optimization not only enhances the model’s predictive capabilities but also enables efficient handling of complex, multi-wave epidemic patterns. This framework sets a promising direction for intelligent, data-driven computational epidemiology and opens avenues for extending the approach to other infectious disease models and real-world intervention strategies.</p>

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Mathematical modeling and computational investigation of the COVID-19 epidemic using wavelet neural networks and coupled optimization

  • 期刊论文

  • 发表日期：

    2025年9月29日

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  • Nimra Shoket,
  • Jamshaid Ul Rahman,
  • Noshaba Zafar

摘要

Artificial Neural Networks (ANNs) have emerged as powerful tools for modeling the highly nonlinear dynamics inherent in epidemiological systems. In particular, the Coronavirus Disease 2019 (COVID-19) pandemic has presented unprecedented challenges due to its multi-wave behavior, variable transmission dynamics, and uncertain external influences. This study introduces a novel computational approach for simulating the generalized COVID-19 epidemic by integrating a Morlet Wavelet Neural Network (MWNN) with a hybrid metaheuristic optimization technique that synergizes Genetic Algorithm (GA) and Adaptive Simulated Annealing (ASA). Motivated by the need to simulate more realistic and adaptable transmission patterns in epidemic modeling, the underlying study incorporates stochastic dynamics and explores three distinct recruitment rate functions: two oscillatory periodic profiles with varying amplitudes and frequencies, and one exponentially decaying non-periodic profile, each reflecting plausible real-world recruitment behaviors. To ensure the theoretical rigor of the model, a comprehensive mathematical analysis is conducted, wherein the existence and uniqueness of solutions are established using the Banach Fixed-Point Theorem through an appropriate contraction mapping, and the positivity of solutions is rigorously verified. The performance of the proposed MWNN-GA–ASA method is thoroughly validated via statistical indicators, including Mean Absolute Error (MAE) and Root Mean Square Error (RMSE), demonstrating excellent accuracy and convergence. Furthermore, comparative analyses against the Non-Standard Finite Difference (NSFD) method are conducted, supported by box plots, Kernel Density Estimates (KDEs), and loss function curves, showcasing superior performance and error consistency. The model’s reliability is further reinforced by the learning of optimal weight vectors and careful tuning of learning rates, batch size, and training epochs, all of which contribute to its robust generalization and precision. The integration of wavelet theory, deep learning, and hybrid optimization not only enhances the model’s predictive capabilities but also enables efficient handling of complex, multi-wave epidemic patterns. This framework sets a promising direction for intelligent, data-driven computational epidemiology and opens avenues for extending the approach to other infectious disease models and real-world intervention strategies.