A mathematical model of coronavirus transmission by using the heuristic computing neural networks

Zulqurnain Sabir; Adi Asmara; Sanaullah Dehraj; Muhammad Asif Zahoor Raja; Gilder Cieza Altamirano; Soheil Salahshour; R Sadat; Mohamed R Ali

doi:10.1016/j.enganabound.2022.10.033

A mathematical model of coronavirus transmission by using the heuristic computing neural networks

Eng Anal Bound Elem. 2023 Jan:146:473-482. doi: 10.1016/j.enganabound.2022.10.033. Epub 2022 Oct 31.

Authors

Zulqurnain Sabir¹, Adi Asmara², Sanaullah Dehraj³, Muhammad Asif Zahoor Raja⁴, Gilder Cieza Altamirano⁵, Soheil Salahshour⁶, R Sadat⁷, Mohamed R Ali⁸

Affiliations

¹ Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan.
² Faculty of Teacher Training and Education, Mathematics Study Program, Universitas Muhammadiyah Bengkulu, Bengkulu, Indonesia.
³ Department of Mathematics and Statistics, Quaid-e-Awam University of Engineering, Science and Technology, 67480 Nawabshah, Pakistan.
⁴ Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan.
⁵ Universidad Nacional Autónoma de Chota, Chota, Perú.
⁶ Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey.
⁷ Department of Mathematics, Zagazig Faculty of Engineering, Zagazig University, Egypt.
⁸ Center of Research, Faculty of Engineering and Technology, Future University in Egypt New Cairo, 11835, Egypt.

Abstract

In this study, the nonlinear mathematical model of COVID-19 is investigated by stochastic solver using the scaled conjugate gradient neural networks (SCGNNs). The nonlinear mathematical model of COVID-19 is represented by coupled system of ordinary differential equations and is studied for three different cases of initial conditions with suitable parametric values. This model is studied subject to seven class of human population N(t) and individuals are categorized as: susceptible S(t), exposed E(t), quarantined Q(t), asymptotically diseased I_A (t), symptomatic diseased I_S (t) and finally the persons removed from COVID-19 and are denoted by R(t). The stochastic numerical computing SCGNNs approach will be used to examine the numerical performance of nonlinear mathematical model of COVID-19. The stochastic SCGNNs approach is based on three factors by using procedure of verification, sample statistics, testing and training. For this purpose, large portion of data is considered, i.e., 70%, 16%, 14% for training, testing and validation, respectively. The efficiency, reliability and authenticity of stochastic numerical SCGNNs approach are analysed graphically in terms of error histograms, mean square error, correlation, regression and finally further endorsed by graphical illustrations for absolute errors in the range of 10^-05 to 10^-07 for each scenario of the system model.

Keywords: COVID-19; Nonlinear; Numerical results; Quarantine; Runge-Kutta scheme; SCGNNs; Scaled conjugate gradient.