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Swarming Computational Techniques for the Influenza Disease System

Sakda Noinang1, Zulqurnain Sabir2, Gilder Cieza Altamirano3, Muhammad Asif Zahoor Raja4, Manuel Jesús Sànchez-Chero5, María-Verónica Seminario-Morales5, Wajaree Weera6,*, Thongchai Botmart6
1 Department of Mathematics Statistics and Computer, Faculty of Science, Ubon Ratchathani University, Ubon Ratchathani, 34190, Thailand
2 Department of Mathematics and Statistics, Hazara University, Mansehra, 21120, Pakistan
3 Universidad Nacional Autónoma de Chota, Cajamarca, 06121, Perú
4 Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin, 64002, Taiwan
5 Universidad Nacional de Frontera, Sullana, Perú
6 Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand
* Corresponding Author: Wajaree Weera. Email:

Computers, Materials & Continua 2022, 73(3), 4851-4868.

Received 04 March 2022; Accepted 25 May 2022; Issue published 28 July 2022


The current study relates to designing a swarming computational paradigm to solve the influenza disease system (IDS). The nonlinear system’s mathematical form depends upon four classes: susceptible individuals, infected people, recovered individuals and cross-immune people. The solutions of the IDS are provided by using the artificial neural networks (ANNs) together with the swarming computational paradigm-based particle swarm optimization (PSO) and interior-point scheme (IPA) that are the global and local search approaches. The ANNs-PSO-IPA has never been applied to solve the IDS. Instead a merit function in the sense of mean square error is constructed using the differential form of each class of the IDS and then optimized by the PSOIPA. The correctness and accuracy of the scheme are observed to perform the comparative analysis of the obtained IDS results with the Adams solutions (reference solutions). An absolute error in suitable measures shows the precision of the proposed ANNs procedures and the optimization efficiency of the PSOIPA. Furthermore, the reliability and competence of the proposed computing method are enhanced through the statistical performances.


Disease; influenza model; reference results; particle swarm optimization; artificial neural networks; interior-point scheme; statistical investigations

Cite This Article

S. Noinang, Z. Sabir, G. C. Altamirano, M. A. Zahoor Raja, M. J. Sànchez-Chero et al., "Swarming computational techniques for the influenza disease system," Computers, Materials & Continua, vol. 73, no.3, pp. 4851–4868, 2022.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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