Novel neuro-stochastic adaptive supervised learning for numerical treatment of nonlinear epidemic delay differential system with impact of double diseases

ABSTRACT

This paper presents a novel neuro-stochastic adaptive processing to investigate the dynamic behavior of the nonlinear SIS epidemic delayed model with the impact of double disease (SIS-EDDM) using the knack of prediction and modeling of artificial neural networks (ANNs) optimized through Levenberg-Marquardt technique (LMT), i.e. ANNs-LMT. The model captures the dynamic progression of individuals in the population, differentiating between those susceptible to infection and affected by two unique viruses. The inclusion of time delays in the differential equations introduces a critical temporal aspect to the model, enhancing its precision in portraying the transmutation process. The reference dataset for ANNs-LMT is produced using the explicit Runge-Kutta method, with variations in the transmission coefficients between susceptible and infective populations, the death rate of infective population caused by diseases, the cure rate of treatment for infected population, vaccination proportional coefficient for the susceptible population, white noise of the environment, and time delay. The designed computing framework of ANNs-LMT is used to determine the numerical solutions of the variants of SIS-EDDM by incorporating the training, testing, and validation samples based adaptive learning processing. The neuro-stochastic adaptive processing of ANNs-LMT is validated by minimal absolute and mean squared errors, coupled with the attainment of nearly optimal regression measures, demonstrating its accuracy and effectiveness.

KEYWORDS:

• Nonlinear delayed differential systems
• explicit Runge-Kutta method
• artificial neural networks
• Levenberg-Marquardt technique
• regression measures

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Additional information

Notes on contributors

Nabeela Anwar

Nabeela Anwar, born in Mandi Bha ud Din, Pakistan, holds an MSc in Mathematics from Govt. Zamindar College Gujrat in 2010, an MPhil in Mathematics from the University of Gujrat in 2014, and a PhD in Mathematics from the University of Gujrat in 2023. Currently serving as an associate lecturer at the University of Narowal, Pakistan. She specializes in multidisciplinary areas such as artificial intelligence, supervised learning, deep learning, computational mathematics, and mathematical modeling of differential equations. With a robust academic background. She has authored about 15 high-impact publications and actively collaborates with renowned professors in her research pursuits. Her expertise extends to the domains of delay differential equations, fractional differential equations, and stochastic differential equations.

Iftikhar Ahmad

Iftikhar Ahmad was born in village Shahaya, Tehsil: Hasssan Abdal District: Atttock, Pakistan. Ahmad has obtained MSc Mathematics degree from Govt. Asghar Mall College Rawalpindi, Pakistan in 1993, MPhil in Mathematics from Quaid-i-Azam, University, Islamabad, Pakistan in 1997 and PhD in field of Inflationary Cosmology from Chinese Academy of Sciences (CAS) Beijing, China, in 2009. Ahmad has served Punjab Higher Education Department as lecturer in 1997 to 2009. After that he has served as Assistant Professor in 2009 to 2017 and Associate Professor from 2017 to 2021, in Department of Mathematics, University of Gujrat, Gujrat, Pakistan. Currently Ahmad is working as Professor/Chairperson Department of Mathematics University of Gujrat, Pakistan. Ahmad has been author of more than 200 high quality, high impact factor publications and have active research collaboration with renewed professors from USA, Germany, Portugal, Spain, Italy, Malaysia, Turkey and Chinese Academy of Sciences. Ahmad is working in multidiscipline inflationary cosmology, artificial intelligent, supervised learning, deep learning, computational mathematics, mathematical modeling of differential equations and partial differential equations, wave propagation.

Adiqa Kausar Kiani

Professor Dr. Adiqa Kausar Kiani has done PhD in economics from QAU Pakistan . Dr. Kiani was awarded the Best University Teacher Award for the year 2009 by the Higher Education Commission. In 2013, Dr. Kiani successfully completed a Fulbright post-doc fellowship to the University of Pennsylvania, Philadelphia where she collaborated with Professor Jere Behrman. She has more than 28 research publications in WOS journals. She also has international exposure and has presented papers at some of the best universities including Massachusetts Institute of Technology (twice), Stanford University and Polytechnique Institute California (twice). Dr. Kiani has attended conferences in Senegal, Turkey, Malaysia, Indonesia, Nepal, Srilanka, Las Vegas, and Cuba to present research papers relating to business and economics. She has successfully supervised 8 PhD and 40 MPhil theses, She is also the member of American Economic Association and many national and international organizations.

Muhammad Shoaib

Muhammad Shoaib is a resident of village Basal of district Attock, Punjab Pakistan. He completed his master’s degree in Mathematics, in 2012 Punjab University Lahore, Pakistan, and Ph.D. Mathematics in 2016 from Riphah International University Islamabad Pakistan. He is currently working as Professor at Yuan Ze University, Taiwan. He has about 200 research publications in international Impact Factor Journals with an impact factor of approximately 450 plus. His area of interest includes mathematical modeling, neural networks, artificial intelligence and implementation of computational techniques based on traditional as well as heuristic paradigms.

Muhammad Asif Zahoor Raja

Muhammad Asif Zahoor Raja was born in 1973 at Sadiqabad, Rawalpindi, Pakistan. He has done his M.Sc. Mathematics degree from Forman Christen College Lahore, Pakistan in 1996, M.Sc. Nuclear Engineering, from Quaid-e-Azam, University, Islamabad, Pakistan in 1999 and Ph.D. Electronic Engineering from International Islamic University, Islamabad, Pakistan in 2011. He is involved in research and development assignment of Engineering and Scientific Commission of Pakistan from 1999 to 2012. He works as Associate Professor in department of Computer and Electrical Engineering, COMSATS University Islamabad, Attock Campus, Attock, Pakistan from 2012 to 2020. Presently working as a full Professor at Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan, R.O.C. Dr. Raja has developed the Fractional least mean square algorithm and computational platform is formulated for the first time for solving fractional differential equation using artificial intelligence techniques during his Ph.D. studies. Dr. Raja has been author of more than 610 publications, out of which 530+ are reputed journal publications with impact factor. Dr. Raja acts as a resource person and gives invited talks on many workshops and conferences held at the national level. His areas of interest are solving linear and nonlinear differential equation of arbitrary order, information security, active noise control system, fractional adaptive signal processing, nonlinear system identification, direction of arrival estimation, cyber security models, economics and Bio-informatics problems.