Artificial neural network procedures for the waterborne spread and control of diseases

Naret Ruttanaprommarin; Zulqurnain Sabir; Rafaél Artidoro Sandoval Núñez; Soheil Salahshour; Juan Luis García Guirao; Wajaree Weera; Thongchai Botmart; Anucha Klamnoi; Naret Ruttanaprommarin; Zulqurnain Sabir; Rafaél Artidoro Sandoval Núñez; Soheil Salahshour; Juan Luis García Guirao; Wajaree Weera; Thongchai Botmart; Anucha Klamnoi

doi:10.3934/math.2023126

AIMS Mathematics

2023, Volume 8, Issue 1: 2435-2452. doi: 10.3934/math.2023126

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Research article

Artificial neural network procedures for the waterborne spread and control of diseases

1.
Department of Science and Mathematics, Faculty of Industry and Technology, Rajamangala University of Technology Isan Sakonnakhon Campus, Sakonnakhon 47160, Thailand
2.
Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
3.
Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551, Al Ain, UAE
4.
Universidad Nacional Autónoma de Chota, Cajamarca, Perú
5.
Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey
6.
Technical University of Cartagena, Applied Mathematics and Statistics Department, Spain
7.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
8.
Department of Applied Mathematics and Statistics, Rajamangala University of Technology Isan, Nakhon Ratchasima 30000, Thailand

Received: 07 July 2022 Revised: 17 September 2022 Accepted: 28 September 2022 Published: 03 November 2022
MSC : 34K50, 92B20

In this study, a nonlinear mathematical SIR system is explored numerically based on the dynamics of the waterborne disease, e.g., cholera, that is used to incorporate the delay factor through the antiseptics for disease control. The nonlinear mathematical SIR system is divided into five dynamics, susceptible X(u), infective Y(u), recovered Z(u) along with the B(u) and C_h(u) be the contaminated water density. Three cases of the SIR system are observed using the artificial neural network (ANN) along with the computational Levenberg-Marquardt backpropagation (LMB) called ANNLMB. The statistical performances of the SIR model are provided by the selection of the data as 74% for authentication and 13% for both training and testing, together with 12 numbers of neurons. The exactness of the designed ANNLMB procedure is pragmatic through the comparison procedures of the proposed and reference results based on the Adam method. The substantiation, constancy, reliability, precision, and ability of the proposed ANNLMB technique are observed based on the state transitions measures, error histograms, regression, correlation performances, and mean square error values.
- SIR system,
- delay term,
- artificial neural network,
- stochastic procedure,
- Levenberg-Marquardt backpropagation
Citation: Naret Ruttanaprommarin, Zulqurnain Sabir, Rafaél Artidoro Sandoval Núñez, Soheil Salahshour, Juan Luis García Guirao, Wajaree Weera, Thongchai Botmart, Anucha Klamnoi. Artificial neural network procedures for the waterborne spread and control of diseases[J]. AIMS Mathematics, 2023, 8(1): 2435-2452. doi: 10.3934/math.2023126

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Abstract

In this study, a nonlinear mathematical SIR system is explored numerically based on the dynamics of the waterborne disease, e.g., cholera, that is used to incorporate the delay factor through the antiseptics for disease control. The nonlinear mathematical SIR system is divided into five dynamics, susceptible X(u), infective Y(u), recovered Z(u) along with the B(u) and C_h(u) be the contaminated water density. Three cases of the SIR system are observed using the artificial neural network (ANN) along with the computational Levenberg-Marquardt backpropagation (LMB) called ANNLMB. The statistical performances of the SIR model are provided by the selection of the data as 74% for authentication and 13% for both training and testing, together with 12 numbers of neurons. The exactness of the designed ANNLMB procedure is pragmatic through the comparison procedures of the proposed and reference results based on the Adam method. The substantiation, constancy, reliability, precision, and ability of the proposed ANNLMB technique are observed based on the state transitions measures, error histograms, regression, correlation performances, and mean square error values.

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