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

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

Zulqurnain Sabir  1 , Adi Asmara  2 , Sanaullah Dehraj  3 , Muhammad Asif Zahoor Raja  4 , Gilder Cieza Altamirano  5 , Soheil Salahshour  6 , R Sadat  7 , Mohamed R Ali  8
Affiliations

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

Zulqurnain Sabir et al. Eng Anal Bound Elem. 2023 Jan.

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 IA (t), symptomatic diseased IS (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.

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Conflict of interest statement

All authors describe that there are no potential conflicts of interest.

Figures

Fig. 1
Fig. 1
Workflow illustrations of the SCGNNs to study the mathematical of COVID-19.
Fig. 2
Fig. 2
The organization of single neuron.
Fig. 3
Fig. 3
SCGNNs for nonlinear system with 16 neurons.
Fig. 4
Fig. 4
MSE and STs to investigate the proposed mathematical model of COVID-19.
Fig. 5
Fig. 5
Valuations and EHs to investigate the proposed mathematical model of COVID-19.
Fig. 6
Fig. 6
Comparison of the result to investigate proposed mathematical model of COVID-19.
Fig. 7
Fig. 7
AE to investigate proposed mathematical model of COVID-19.
See this image and copyright information in PMC

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