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Akter M, Nurunnahar, Ullah MS, Meetei MZ, Zaagan AA, Mahnashi AM. An innovative fractional-order evolutionary game theoretical study of personal protection, quarantine, and isolation policies for combating epidemic diseases. Sci Rep 2024; 14:14464. [PMID: 38914575 DOI: 10.1038/s41598-024-61211-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2024] [Accepted: 05/02/2024] [Indexed: 06/26/2024] Open
Abstract
This study uses imposed control techniques and vaccination game theory to study disease dynamics with transitory or diminishing immunity. Our model uses the ABC fractional-order derivative mechanism to show the effect of non-pharmaceutical interventions such as personal protection or awareness, quarantine, and isolation to simulate the essential control strategies against an infectious disease spread in an infinite and uniformly distributed population. A comprehensive evolutionary game theory study quantified the significant influence of people's vaccination choices, with government forces participating in vaccination programs to improve obligatory control measures to reduce epidemic spread. This model uses the intervention options described above as a control strategy to reduce disease prevalence in human societies. Again, our simulated results show that a combined control strategy works exquisitely when the disease spreads even faster. A sluggish dissemination rate slows an epidemic outbreak, but modest control techniques can reestablish a disease-free equilibrium. Preventive vaccination regulates the border between the three phases, while personal protection, quarantine, and isolation methods reduce disease transmission in existing places. Thus, successfully combining these three intervention measures reduces epidemic or pandemic size, as represented by line graphs and 3D surface diagrams. For the first time, we use a fractional-order derivate to display the phase-portrayed trajectory graph to show the model's dynamics if immunity wanes at a specific pace, considering various vaccination cost and effectiveness settings.
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Affiliation(s)
- Masuda Akter
- Department of Mathematics, Feni University, Feni, 3900, Bangladesh
| | - Nurunnahar
- Department of Mathematics, Feni University, Feni, 3900, Bangladesh
| | | | - Mutum Zico Meetei
- Department of Mathematics, College of Science, Jazan University, 45142, Jazan, P.O. Box 114, Kingdom of Saudi Arabia.
| | - Abdullah A Zaagan
- Department of Mathematics, College of Science, Jazan University, 45142, Jazan, P.O. Box 114, Kingdom of Saudi Arabia
| | - Ali M Mahnashi
- Department of Mathematics, College of Science, Jazan University, 45142, Jazan, P.O. Box 114, Kingdom of Saudi Arabia
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Ullah MS, Kabir KA. Behavioral game of quarantine during the monkeypox epidemic: Analysis of deterministic and fractional order approach. Heliyon 2024; 10:e26998. [PMID: 38495200 PMCID: PMC10943359 DOI: 10.1016/j.heliyon.2024.e26998] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2023] [Revised: 02/06/2024] [Accepted: 02/22/2024] [Indexed: 03/19/2024] Open
Abstract
This work concerns the epidemiology of infectious diseases like monkeypox (mpox) in humans and animals. Our models examine transmission scenarios, including transmission dynamics between humans, animals, and both. We approach this using evolutionary game theory, specifically the intervention game-theoretical (IGT) framework, to study how human behavior can mitigate disease transmission without perfect vaccines and treatments. To do this, we use non-pharmaceutical intervention, namely the quarantine policy, which demonstrates the delayed effect of the epidemic. Additionally, we contemplate quarantine-based behavioral intervention policies in deterministic and fractional-order models to show behavioral impact in the context of the memory effect. Firstly, we extensively analyzed the model's positivity and boundness of the solution, reproduction number, disease-free and endemic equilibrium, possible stability, existence, concavity, and Ulam-Hyers stability for the fractional order. Subsequently, we proceeded to present a numerical analysis that effectively illustrates the repercussions of varying quarantine-related factors, information probability, and protection probability. We aimed to comprehensively examine the effects of non-pharmaceutical interventions on disease control, which we conveyed through line graphs and 2D heat maps. Our findings underscored the significant influence of strict quarantine measures and the protection of both humans and animals in mitigating disease outbreaks. These measures not only significantly curtailed the spread of the disease but also delayed the occurrence of the epidemic's peak. Conversely, when quarantine maintenance policies were implemented at lower rates and protection levels diminished, we observed contrasting outcomes that exacerbated the situation. Eventually, our analysis revealed the emergence of animal reservoirs in cases involving disease transmission between humans and animals.
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Affiliation(s)
| | - K.M. Ariful Kabir
- Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, 1000, Bangladesh
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Ullah MS, Kamrujjaman M, Kabir KMA. Understanding the relationship between stay-at-home measures and vaccine shortages: a conventional, heterogeneous, and fractional dynamic approach. JOURNAL OF HEALTH, POPULATION, AND NUTRITION 2024; 43:32. [PMID: 38424608 DOI: 10.1186/s41043-024-00505-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2023] [Accepted: 01/13/2024] [Indexed: 03/02/2024]
Abstract
In light of the global prevalence of a highly contagious respiratory disease, this study presents a novel approach to address the pressing and unanticipated issues by introducing a modified vaccination and lockdown-centered epidemic model. The rapid spread of the disease is attributed to viral transmissibility, the emergence of new strains (variants), lack of immunization, and human unawareness. This study aims to provide policymakers with crucial insights for making informed decisions regarding lockdown strategies, vaccine availability, and other control measures. The research adopts three types of models: deterministic, heterogeneous, and fractional-order dynamics, on both theoretical and numerical approaches. The heterogeneous network considers varying connectivity and interaction patterns among individuals, while the ABC fractional-order derivatives analyze the impact of integer-order control in different semi-groups. An extensive theoretical analysis is conducted to validate the proposed model. A comprehensive numerical investigation encompasses deterministic, stochastic, and ABC fractional-order derivatives, considering the combined effects of an effective vaccination program and non-pharmaceutical interventions, such as lockdowns and shutdowns. The findings of this research are expected to be valuable for policymakers in different countries, helping them implement dynamic strategies to control and eradicate the epidemic effectively.
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Affiliation(s)
| | | | - K M Ariful Kabir
- Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh
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Abstract
This work deals with a new finite time stability (FTS) of neutral fractional order systems with time delay (NFOTSs). In light of this, FTSs of NFOTSs are demonstrated in the literature using the Gronwall inequality. The innovative aspect of our proposed study is the application of fixed point theory to show the FTS of NFOTSs. Finally, using two examples, the theoretical contributions are confirmed and substantiated.
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Kharrat M, Arfaoui H. A New Stabled Relaxation Method for Pricing European Options Under the Time-Fractional Vasicek Model. COMPUTATIONAL ECONOMICS 2022; 61:1745-1763. [PMID: 35572160 PMCID: PMC9075931 DOI: 10.1007/s10614-022-10264-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Accepted: 03/29/2022] [Indexed: 05/24/2023]
Abstract
Our objective is to solve the time-fractional Vasicek model for European options with a new stabled relaxation method. This new approach is based on the splitting method. Some numerical tests are presented to show the stability and the reliability of our approach with the theory of options.
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Affiliation(s)
- Mohamed Kharrat
- Mathematics Department, College of Science, Jouf University, Sakaka, Saudi Arabia
| | - Hassen Arfaoui
- Mathematics Department, College of Science, Jouf University, Sakaka, Saudi Arabia
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Application of the Fractional Riccati Equation for Mathematical Modeling of Dynamic Processes with Saturation and Memory Effect. FRACTAL AND FRACTIONAL 2022. [DOI: 10.3390/fractalfract6030163] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this study, the model Riccati equation with variable coefficients as functions, as well as a derivative of a fractional variable order (VO) of the Gerasimov-Caputo type, is used to approximate the data for some physical processes with saturation. In particular, the proposed model is applied to the description of solar activity (SA), namely the number of sunspots observed over the past 25 years. It is also used to describe data from Johns Hopkins University on coronavirus infection COVID-19, in particular data on the Russian Federation and the Republic of Uzbekistan. Finally, it is used to study issues related to seismic activity, in particular, the description of data on the volumetric activity of Radon (RVA). The Riccati equation used in the mathematical model was numerically solved by constructing an implicit finite difference scheme (IFDS) and its implementation by the modified Newton method (MNM). The calculated curves obtained in the study are compared with known experimental data. It is shown that if the model parameters are chosen appropriately, the model curves will give results that correlate well with real experimental data. Moreover, with other parameters of the model, it is possible to make some prediction about the possible course of the considered processes.
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Ullah MS, Higazy M, Ariful Kabir KM. Modeling the epidemic control measures in overcoming COVID-19 outbreaks: A fractional-order derivative approach. CHAOS, SOLITONS, AND FRACTALS 2022; 155:111636. [PMID: 34866811 PMCID: PMC8626290 DOI: 10.1016/j.chaos.2021.111636] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2021] [Revised: 11/09/2021] [Accepted: 11/15/2021] [Indexed: 05/31/2023]
Abstract
Novel coronavirus named SARS-CoV-2 is one of the global threads and uncertain challenges worldwide faced at present. It has stroke rapidly around the globe due to viral transmissibility, new variants (strains), and human unconsciousness. Lack of adequate and reliable vaccination and proper treatment, control measures such as self-protection, physical distancing, lockdown, quarantine, and isolation policy plays an essential role in controlling and reducing the pandemic. Decisions on enforcing various control measures should be determined based on a theoretical framework and real-data evidence. We deliberate a general mathematical control measures epidemic model consisting of lockdown, self-protection, physical distancing, quarantine, and isolation compartments. Then, we investigate the proposed model through Caputo fractional order derivative. Fixed point theory has been used to analyze the Caputo fractional-order derivative model's existence and uniqueness solutions, whereas the Adams-Bashforth-Moulton numerical scheme was applied for numerical simulation. Driven by extensive theoretical analysis and numerical simulation, this work further illuminates the substantial impact of various control measures.
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Affiliation(s)
- Mohammad Sharif Ullah
- Department of Mathematics, Feni University, Feni, Bangladesh
- Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh
| | - M Higazy
- Department of Mathematics, College of Science, Taif University, PO Box 11099, Taif 21944, Saudi Arabia
- Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, Egypt
| | - K M Ariful Kabir
- Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh
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Arfaoui H, Ben Makhlouf A. Some results for a class of two-dimensional fractional hyperbolic differential systems with time delay. JOURNAL OF APPLIED MATHEMATICS & COMPUTING 2021; 68:2389-2405. [PMID: 34512222 PMCID: PMC8423604 DOI: 10.1007/s12190-021-01625-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/05/2021] [Revised: 07/13/2021] [Accepted: 08/28/2021] [Indexed: 06/13/2023]
Abstract
This work deals with the existence and uniqueness of global solution and finite time stability of fractional partial hyperbolic differential systems (FPHDSs). Using the fixed-point approach, the existence and uniqueness of global solution is studied and an estimation of solution is given. Moreover, some sufficient conditions for the finite time stability of FPHDSs are established. Numerical experiments illustrate the Stability result.
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Affiliation(s)
- Hassen Arfaoui
- Department of Mathematics, College of Science, Jouf University, Sakaka, Saudi Arabia
- LAMSIN-ENIT, Université de Tunis El Manar, Tunis, Tunisia
| | - Abdellatif Ben Makhlouf
- Department of Mathematics, College of Science, Jouf University, Sakaka, Saudi Arabia
- Department of Mathematics, Faculty of Sciences of Sfax, Sfax, Tunisia
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