A machine learning solutions approach of a time-delayed stochastic $ \tilde{S}\tilde{E}\tilde{I}\tilde{R}\tilde{V} $ model

Mostafa Zahri; Inayat khan; Rahat Zarin; Amir khan; Rukhsar Ikram; Mostafa Zahri; Inayat khan; Rahat Zarin; Amir khan; Rukhsar Ikram

doi:10.3934/nhm.2025030

Networks and Heterogeneous Media

2025, Volume 20, Issue 2: 701-731. doi: 10.3934/nhm.2025030

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A machine learning solutions approach of a time-delayed stochastic $ \tilde{S}\tilde{E}\tilde{I}\tilde{R}\tilde{V} $ model

1.
College of Sciences, Department of Mathematics, RGs MASEP and BioInformatics FG, University of Sharjah, United Arab Emirates
2.
Department of Mathematics and Statistics, University of Swat, KPK, Pakistan
3.
Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand

Received: 02 March 2025 Revised: 20 May 2025 Accepted: 23 May 2025 Published: 12 June 2025

In this work, we analyze the dynamics of a stochastic $ \tilde{S}\tilde{E}\tilde{I}\tilde{R}\tilde{V} $ model with a time delay. We mainly investigate the time delay's influence on these classes' asymptotic behavior. Furthermore, we examine the existence and stability of disease-free and endemic equilibrium points. To better understand the parameter's effects on the spread of an epidemic, we integrate artificial neural networks with the Bayesian regularization method. Additionally, leveraging physics-informed artificial intelligence (AI) and specialized machine training, we develop an advanced framework for solving systems of partial differential equations (PDEs). This approach enhances the accuracy of predictions and facilitates the optimal control and effective implementation of real-world epidemic management strategies.
- epidemic stochastic model,
- COVID-19,
- time delay dynamics,
- stochastic stability,
- Bayesian regularization,
- machine learning,
- artificial neural networks
Citation: Mostafa Zahri, Inayat khan, Rahat Zarin, Amir khan, Rukhsar Ikram. A machine learning solutions approach of a time-delayed stochastic $ \tilde{S}\tilde{E}\tilde{I}\tilde{R}\tilde{V} $ model[J]. Networks and Heterogeneous Media, 2025, 20(2): 701-731. doi: 10.3934/nhm.2025030

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Abstract

In this work, we analyze the dynamics of a stochastic $ \tilde{S}\tilde{E}\tilde{I}\tilde{R}\tilde{V} $ model with a time delay. We mainly investigate the time delay's influence on these classes' asymptotic behavior. Furthermore, we examine the existence and stability of disease-free and endemic equilibrium points. To better understand the parameter's effects on the spread of an epidemic, we integrate artificial neural networks with the Bayesian regularization method. Additionally, leveraging physics-informed artificial intelligence (AI) and specialized machine training, we develop an advanced framework for solving systems of partial differential equations (PDEs). This approach enhances the accuracy of predictions and facilitates the optimal control and effective implementation of real-world epidemic management strategies.

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