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Li S, Samreen, Ullah S, Riaz MB, Awwad FA, Teklu SW. Global dynamics and computational modeling approach for analyzing and controlling of alcohol addiction using a novel fractional and fractal-fractional modeling approach. Sci Rep 2024; 14:5065. [PMID: 38429318 DOI: 10.1038/s41598-024-54578-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2023] [Accepted: 02/14/2024] [Indexed: 03/03/2024] Open
Abstract
In recent years, alcohol addiction has become a major public health concern and a global threat due to its potential negative health and social impacts. Beyond the health consequences, the detrimental consumption of alcohol results in substantial social and economic burdens on both individuals and society as a whole. Therefore, a proper understanding and effective control of the spread of alcohol addictive behavior has become an appealing global issue to be solved. In this study, we develop a new mathematical model of alcohol addiction with treatment class. We analyze the dynamics of the alcohol addiction model for the first time using advanced operators known as fractal-fractional operators, which incorporate two distinct fractal and fractional orders with the well-known Caputo derivative based on power law kernels. The existence and uniqueness of the newly developed fractal-fractional alcohol addiction model are shown using the Picard-Lindelöf and fixed point theories. Initially, a comprehensive qualitative analysis of the alcohol addiction fractional model is presented. The possible equilibria of the model and the threshold parameter called the reproduction number are evaluated theoretically and numerically. The boundedness and biologically feasible region for the model are derived. To assess the stability of the proposed model, the Ulam-Hyers coupled with the Ulam-Hyers-Rassias stability criteria are employed. Moreover, utilizing effecting numerical schemes, the models are solved numerically and a detailed simulation and discussion are presented. The model global dynamics are shown graphically for various values of fractional and fractal dimensions. The present study aims to provide valuable insights for the understanding the dynamics and control of alcohol addiction within a community.
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Affiliation(s)
- Shuo Li
- School of Mathematics and Data Sciences, Changji University, Changji, 831100, Xinjiang, People's Republic of China
| | - Samreen
- Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Khyber Pakhtunkhwa, Pakistan
| | - Saif Ullah
- Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa, Pakistan
| | - Muhammad Bilal Riaz
- IT4Innovations, VSB -Technical University of Ostrava, Ostrava, Czech Republic
- Department of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon
| | - Fuad A Awwad
- Department of Quantitative analysis, College of Business Administration, King Saud University, P.O. Box 71115, Riyadh, 11587, Saudi Arabia
| | - Shewafera Wondimagegnhu Teklu
- Department of Mathematics, College of Natural and Computational Scieces, Debre Berhan University, 445, Debre Berhan, Ethiopia.
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Adom-Konadu A, Bonyah E, Sackitey AL, Anokye M, Asamoah JKK. A fractional order Monkeypox model with protected travelers using the fixed point theorem and Newton polynomial interpolation. Healthc Anal (N Y) 2023; 3:100191. [PMID: 37214737 PMCID: PMC10167817 DOI: 10.1016/j.health.2023.100191] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/24/2023] [Revised: 03/18/2023] [Accepted: 04/29/2023] [Indexed: 05/24/2023]
Abstract
This study formulates a Monkeypox model with protected travelers. The fixed point theorem is used to obtain the existence and uniqueness of the solution with Ulam-Hyers stability for the analysis of the solution to the model. The Newton polynomial interpolation scheme is employed to solve an approximate solution of the fractional Monkeypox model. The numerical simulations and the graphical representations suggest that the fractional order affects the dynamics of the Monkeypox. The fractional order shows other underlining transmission trends of the Monkeypox disease. We conclude that the result obtained for each compartment conforms to reality as the fractional order approaches unity.
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Affiliation(s)
- Agnes Adom-Konadu
- Department of Mathematics, University of Cape Coast, Cape Coast, Ghana
| | - Ebenezer Bonyah
- Department of Mathematics Education, Akenten Appiah-Menka University of Skills Training and Entrepreneurial Development, Kumasi, Ghana
- Department of Mathematics, Faculty of Science and Technology Universitas Airlangga, Surabaya 60115, Indonesia
- Department of Mathematics and Applied Mathematics, University of Johannesburg, Johannesburg 2006, South Africa
| | | | - Martin Anokye
- Department of Mathematics, University of Cape Coast, Cape Coast, Ghana
| | - Joshua Kiddy K Asamoah
- Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
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Singh R, Tiwari P, Band SS, Rehman AU, Mahajan S, Ding Y, Liu X, Pandit AK. Impact of quarantine on fractional order dynamical model of Covid-19. Comput Biol Med 2022; 151:106266. [PMID: 36395591 PMCID: PMC9660264 DOI: 10.1016/j.compbiomed.2022.106266] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2022] [Revised: 10/12/2022] [Accepted: 10/30/2022] [Indexed: 11/11/2022]
Abstract
In this paper, a Covid-19 dynamical transmission model of a coupled non-linear fractional differential equation in the Atangana-Baleanu Caputo sense is proposed. The basic dynamical transmission features of the proposed system are briefly discussed. The qualitative as well as quantitative results on the existence and uniqueness of the solutions are evaluated through the fixed point theorem. The Ulam-Hyers stability analysis of the suggested system is established. The two-step Adams-Bashforth-Moulton (ABM) numerical method is employed to find its numerical solution. The numerical simulation is performed to accesses the impact of various biological parameters on the dynamics of Covid-19 disease.
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Affiliation(s)
- Ram Singh
- Baba Ghulam Shah Badshah University Rajouri, 185234, India,Corresponding authors
| | - Prayag Tiwari
- School of Information Technology, Halmstad University, Sweden,Corresponding authors
| | - Shahab S. Band
- Future Technology Research Center, College of Future, National Yunlin University of Science and Technology, Douliou, Taiwan, ROC,Corresponding authors
| | | | - Shubham Mahajan
- School of Electronic and Communication, Shri Mata Vaishno Devi University, Katra, 182320, India,Ajeenka D Y University, Pune, Maharashtra, India,iNurture Education Solutions Pvt. Ltd., Bangalore, India
| | - Yijie Ding
- Yangtze Delta Region Institute (Quzhou), University of Electronic Science and Technology of China, Quzhou, 324000, China
| | - Xiaobin Liu
- Department of Nephrology, The Affiliated Wuxi People’s Hospital of Nanjing Medical University, 214023, Wuxi, China,Corresponding authors
| | - Amit Kant Pandit
- School of Electronic and Communication, Shri Mata Vaishno Devi University, Katra, 182320, India
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Alshomrani AS, Ullah MZ, Baleanu D. Caputo SIR model for COVID-19 under optimized fractional order. Adv Differ Equ 2021; 2021:185. [PMID: 33777127 PMCID: PMC7988647 DOI: 10.1186/s13662-021-03345-5] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2020] [Accepted: 03/14/2021] [Indexed: 05/23/2023]
Abstract
Everyone is talking about coronavirus from the last couple of months due to its exponential spread throughout the globe. Lives have become paralyzed, and as many as 180 countries have been so far affected with 928,287 (14 September 2020) deaths within a couple of months. Ironically, 29,185,779 are still active cases. Having seen such a drastic situation, a relatively simple epidemiological SIR model with Caputo derivative is suggested unlike more sophisticated models being proposed nowadays in the current literature. The major aim of the present research study is to look for possibilities and extents to which the SIR model fits the real data for the cases chosen from 1 April to 15 March 2020, Pakistan. To further analyze qualitative behavior of the Caputo SIR model, uniqueness conditions under the Banach contraction principle are discussed and stability analysis with basic reproduction number is investigated using Ulam-Hyers and its generalized version. The best parameters have been obtained via the nonlinear least-squares curve fitting technique. The infectious compartment of the Caputo SIR model fits the real data better than the classical version of the SIR model (Brauer et al. in Mathematical Models in Epidemiology 2019). Average absolute relative error under the Caputo operator is about 48% smaller than the one obtained in the classical case ( ν = 1 ). Time series and 3D contour plots offer social distancing to be the most effective measure to control the epidemic.
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Affiliation(s)
- Ali S. Alshomrani
- Department of Mathematics, King Abdul Aziz University, Jeddah, Saudi Arabia
| | - Malik Z. Ullah
- Department of Mathematics, King Abdul Aziz University, Jeddah, Saudi Arabia
| | - Dumitru Baleanu
- Department of Mathematics, Cankaya University, Öǧretmenler Cad. 1406530, Ankara, Turkey
- Institute of Space Sciences, Magurele, Bucharest, Romania
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
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Ahmed I, Baba IA, Yusuf A, Kumam P, Kumam W. Analysis of Caputo fractional-order model for COVID-19 with lockdown. Adv Differ Equ 2020; 2020:394. [PMID: 32834819 PMCID: PMC7396944 DOI: 10.1186/s13662-020-02853-0] [Citation(s) in RCA: 33] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2020] [Accepted: 07/23/2020] [Indexed: 05/19/2023]
Abstract
One of the control measures available that are believed to be the most reliable methods of curbing the spread of coronavirus at the moment if they were to be successfully applied is lockdown. In this paper a mathematical model of fractional order is constructed to study the significance of the lockdown in mitigating the virus spread. The model consists of a system of five nonlinear fractional-order differential equations in the Caputo sense. In addition, existence and uniqueness of solutions for the fractional-order coronavirus model under lockdown are examined via the well-known Schauder and Banach fixed theorems technique, and stability analysis in the context of Ulam-Hyers and generalized Ulam-Hyers criteria is discussed. The well-known and effective numerical scheme called fractional Euler method has been employed to analyze the approximate solution and dynamical behavior of the model under consideration. It is worth noting that, unlike many studies recently conducted, dimensional consistency has been taken into account during the fractionalization process of the classical model.
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Affiliation(s)
- Idris Ahmed
- KMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140 Thailand
- KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140 Thailand
- Department of Mathematics and Computer Science, Sule Lamido University, P.M.B 048, Kafin-Hausa, Jigawa State Nigeria
| | - Isa Abdullahi Baba
- Department of Mathematical Science, Bayero University Kano, Kano, Nigeria
| | - Abdullahi Yusuf
- Department of Computer Engineering, Biruni University, Istanbul, 34010 Turkey
- Department of Mathematics, Federal University Dutse, Jigawa, 7156 Nigeria
| | - Poom Kumam
- KMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140 Thailand
- KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140 Thailand
| | - Wiyada Kumam
- Program in Applied Statistics, Department of Mathematics and Computer Science, Rajamangala University of Technology Thanyaburi, Thanyaburi, Pathumthani 12110 Thailand
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