Recent years have seen significant advancement in epidemiology using stochastic intelligent schemes, especially those based on feed-forward artificial neural networks (NN). These schemes address the complexity and nonlinearity of the coupled epidemic model based on the differential system, which offers an efficient framework for examining the dynamics of epidemic diseases. In light of the widespread use of these schemes, the current study proposes a swarming-optimized neuro-heuristic procedure that solves the Susceptible, Infected, and Recovered i.e. SIR nonlinear system based on Dengue fever spread with the computational efficiency of a single-layer feed-forward artificial neural network. Particle Swarm Optimization (PSO) a global search strategy in the hybridization of Sequential Quadratic Programming (SQP) was employed for optimization of the fitness function integrated with an effective Mexican hat wavelet activation function i.e. (MHW-NN-PSO-SQP). The MHW-ANN-based fitness function is accessed using the nonlinear coupled differential equations and the initial conditions of the SIR-coupled system. The results produced by the proposed approach are compared with the RK numerical solver and the MWNN-GA-IPA solver to solve the nonlinear SIR system based on Dengue fever spread. Absolute error, mean square error, and mean absolute deviation is used to verify the accuracy and consistency of the calculated scheme. Moreover, the thorough statistical study offers proof of the robustness, stability, and convergence of the planned system. The overlap outcomes of the proposed, RK based numerical solver ANN-GA-SQM and the MWANN-GA-IPA confirm the accuracy of the proposed scheme, while the AE values for the best and mean solutions are in the range 9.99 × 10–16 to 2.00 × 10–14, 9.99 × 10–16 to 4.01 × 10–14, 3.00 × 10–13 to 1.00 × 10–12 and 3.04 × 10–17 to 4.00 × 10–15, 1.00 × 10–13 to 1.00 × 10–15 for X(t), Y(t) and Z(t) respectively. The statistical mean square error is in the range 5.92 × 10–06 to 1.26 × 10–09 and the mean absolute deviation values are in the range 9.87 × 10–06 to 1.44 × 10–11. The global statistical operators and the statistical min, mean and std values further confirm the proposed scheme's stability, reliability, and convergence.

Swarm-optimized numerical investigation of dengue fever model

期刊论文
发表日期：

2025年9月29日

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Farhad Muhammad Riaz,
Raja Muhammad Shamayel Ullah,
Areej Alasiry,
Mehrez Marzougui,
Junaid Ali Khan

摘要

Recent years have seen significant advancement in epidemiology using stochastic intelligent schemes, especially those based on feed-forward artificial neural networks (NN). These schemes address the complexity and nonlinearity of the coupled epidemic model based on the differential system, which offers an efficient framework for examining the dynamics of epidemic diseases. In light of the widespread use of these schemes, the current study proposes a swarming-optimized neuro-heuristic procedure that solves the Susceptible, Infected, and Recovered i.e. SIR nonlinear system based on Dengue fever spread with the computational efficiency of a single-layer feed-forward artificial neural network. Particle Swarm Optimization (PSO) a global search strategy in the hybridization of Sequential Quadratic Programming (SQP) was employed for optimization of the fitness function integrated with an effective Mexican hat wavelet activation function i.e. (MHW-NN-PSO-SQP). The MHW-ANN-based fitness function is accessed using the nonlinear coupled differential equations and the initial conditions of the SIR-coupled system. The results produced by the proposed approach are compared with the RK numerical solver and the MWNN-GA-IPA solver to solve the nonlinear SIR system based on Dengue fever spread. Absolute error, mean square error, and mean absolute deviation is used to verify the accuracy and consistency of the calculated scheme. Moreover, the thorough statistical study offers proof of the robustness, stability, and convergence of the planned system. The overlap outcomes of the proposed, RK based numerical solver ANN-GA-SQM and the MWANN-GA-IPA confirm the accuracy of the proposed scheme, while the AE values for the best and mean solutions are in the range 9.99 × 10^–16 to 2.00 × 10^–14, 9.99 × 10^–16 to 4.01 × 10^–14, 3.00 × 10^–13 to 1.00 × 10^–12 and 3.04 × 10^–17 to 4.00 × 10^–15, 1.00 × 10^–13 to 1.00 × 10^–15 for X(t), Y(t) and Z(t) respectively. The statistical mean square error is in the range 5.92 × 10^–06 to 1.26 × 10^–09 and the mean absolute deviation values are in the range 9.87 × 10^–06 to 1.44 × 10^–11. The global statistical operators and the statistical min, mean and std values further confirm the proposed scheme's stability, reliability, and convergence.