Yazar "Jamil, Saba" seçeneğine göre listele

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    Computational and stability analysis of Ebola virus epidemic model with piecewise hybrid fractional operator
    (Public Library Science, 2024) Nisar, Kottakkaran Sooppy; Farman, Muhammad; Jamil, Khadija; Akgul, Ali; Jamil, Saba
    In this manuscript, we developed a nonlinear fractional order Ebola virus with a novel piecewise hybrid technique to observe the dynamical transmission having eight compartments. The existence and uniqueness of a solution of piecewise derivative is treated for a system with Arzel'a-Ascoli and Schauder conditions. We investigate the effects of classical and modified fractional calculus operators, specifically the classical Caputo piecewise operator, on the behavior of the model. A model shows that a completely continuous operator is uniformly continuous, and bounded according to the equilibrium points. The reproductive number R0 is derived for the biological feasibility of the model with sensitivity analysis with different parameters impact on the model. Sensitivity analysis is an essential tool for comprehending how various model parameters affect the spread of illness. Through a methodical manipulation of important parameters and an assessment of their impact on Ro, we are able to learn more about the resiliency and susceptibility of the model. Local stability is established with next Matignon method and global stability is conducted with the Lyapunov function for a feasible solution of the proposed model. In the end, a numerical solution is derived with Newton's polynomial technique for a piecewise Caputo operator through simulations of the compartments at various fractional orders by using real data. Our findings highlight the importance of fractional operators in enhancing the accuracy of the model in capturing the intricate dynamics of the disease. This research contributes to a deeper understanding of Ebola virus dynamics and provides valuable insights for improving disease modeling and public health strategies.
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    Fractional order age dependent Covid-19 model: An equilibria and quantitative analysis with modeling
    (Elsevier, 2023) Jamil, Saba; Farman, Muhammad; Akgul, Ali; Saleem, Muhammad Umer; Hincal, Evren; El Din, Sayed M.
    The presence of different age groups in the populations being studied requires us to develop models that account for varying susceptibilities based on age. This complexity adds a layer of difficulty to predicting outcomes accurately. Essentially, there are three main age categories: 0 - 19 years, 20 - 64 years, and > 64 years. However, in this article, we only focus on two age groups (20 - 64 years and > 64 years) because the age category 0 - 19 years is generally perceived as having a lower susceptibility to the virus due to its consistently low infection rate during the pandemic period of this research, particularly in the countries being examined. In this paper, we presented an age-dependent epidemic model for the COVID-19 Outbreak in Kuwait, France, and Cameroon in the fractal-fractional (FF) sense of derivative with the Mittag-Leffler kernel. The study includes positivity, stability, existence results, uniqueness, stability, and numerical simulations. Globally, the age-dependent COVID-19 fractal fractional model is examined using the first and second derivatives of Lyapunov. Fixed point theory is used to derive the existence and uniqueness of the fractional-order model. The numerical scheme of this paper is based on the Newton polynomial and is tested for a particular case with numerical values from Kuwait, France, and Cameroon. In our analysis, we explore the significance of these distinct parameters incorporated into the model, focusing particularly on the impact of vaccination and fractional order on the progression of the epidemic. The results are getting closer to the classical case for the orders reaching 1 while all other solutions are different with the same behavior. Consequently, the fractal fractional order model provides more substantial insights into the epidemic disease. We open a novel viewpoint on enhancing an age-dependent model and applying it to real-world data and parameters. Such a study will help determine the behavior of the virus and disease control methods for a population.
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    Mathematical study of fractal-fractional leptospirosis disease in human and rodent populations dynamical transmission
    (Elsevier, 2024) Farman, populations dynamical Muhammad; Jamil, Saba; Nisar, Kottakkaran Sooppy; Akgul, Ali
    In both industrialized and developing nations, leptospirosis is one of the most underdiagnosed and underreported diseases. It is known that people are more likely to contract a disease depending on their employment habits and the environment they live in, which varies from community to community. The absence of global data for morbidity and mortality has contributed to leptospirosis' neglected disease status even though it is a life -threatening illness and is widely acknowledged as a significant cause of pulmonary hemorrhage syndrome. This study aims to examine the impact of rodent -borne leptospirosis on the human population by constructing and evaluating a compartmental mathematical model using fractional -order differential equations. The model considers both the presence of disease -causing agents in the environment and the rate of human infection resulting from interactions with infected rodents and the environment. Through this approach, the research investigates the dynamics and implications of leptospirosis transmission in the context of human -rodent interactions and environmental factors. We create a fractal -fractional model using the mittag-leffler kernel. The positivity and boundedness of solutions are first discussed. The model equilibria and fundamental reproduction number are then presented. With the use of the Lyapunov function method, the solutions are subjected to global stability analysis. The fixed-point theory is used to derive the fractional -order model's existence and uniqueness. Solutions are produced using a two-step Lagrange polynomial in the generalized form of the Mittag-Leffler kernel to explore the effect of the fractional operator with numerical simulations, which shows the influence of the sickness due to the effect of different parameters involved. Such a study will aid in the development of control strategies to combat the disease in the community and an understanding of the behavior of the Leptospira virus.
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    Qualitative analysis and chaotic behavior of respiratory syncytial virus infection in human with fractional operator
    (Nature Portfolio, 2024) Jamil, Saba; Bariq, Abdul; Farman, Muhammad; Nisar, Kottakkaran Sooppy; Akguel, Ali; Saleem, Muhammad Umer
    Respiratory syncytial virus (RSV) is the cause of lung infection, nose, throat, and breathing issues in a population of constant humans with super-spreading infected dynamics transmission in society. This research emphasizes on examining a sustainable fractional derivative-based approach to the dynamics of this infectious disease. We proposed a fractional order to establish a set of fractional differential equations (FDEs) for the time-fractional order RSV model. The equilibrium analysis confirmed the existence and uniqueness of our proposed model solution. Both sensitivity and qualitative analysis were employed to study the fractional order. We explored the Ulam-Hyres stability of the model through functional analysis theory. To study the influence of the fractional operator and illustrate the societal implications of RSV, we employed a two-step Lagrange polynomial represented in the generalized form of the Power-Law kernel. Also, the fractional order RSV model is demonstrated with chaotic behaviors which shows the trajectory path in a stable region of the compartments. Such a study will aid in the understanding of RSV behavior and the development of prevention strategies for those who are affected. Our numerical simulations show that fractional order dynamic modeling is an excellent and suitable mathematical modeling technique for creating and researching infectious disease models.
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    Qualitative analysis and chaotic behavior of respiratory syncytial virus infection in human with fractional operator (vol 14, 2175, 2024)
    (Nature Portfolio, 2024) Jamil, Saba; Bariq, Abdul; Farman, Muhammad; Nisar, Kottakkaran Sooppy; Akguel, Ali; Saleem, Muhammad Umer
    [Abstract Not Available]
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    Qualitative and quantitative analysis of a fractal fractional HIV/AIDS model
    (Elsevier, 2023) Jamil, Saba; Farman, Muhammad; Akgul, Ali
    The fractal-fractional derivative is a type of fractional derivative that is more broadly applicable. This method is used to investigate a variety of real-world issues. This work focuses on investigating a fractional derivative-based sustainable strategy for the dynamics of HIV/AIDS. For the representation of a time-fractional order HIV/AIDS model, we presented a system of FDEs. The suggested model's uniqueness and existence are revealed through equilibrium analysis. Analysis of the fractional order is accomplished using both sensitivity analysis and qualitative analysis. The first and second derivative tests are used to validate the analysis of the Lyapunov function for global stability. Solutions are produced using a two-step Lagrange polynomial in the generalized form of the Mlittag-Lefler kernel to analyze the influence of the fractional operator, which illustrates the impact of HIV/AIDS on society. Such an inquiry will help in the comprehension of HIV/AIDS behavior and the creation of preventative measures for the infected. Graphical representations of sensitive criteria that illustrate how to reduce and eradicate HIV/AIDS in society are provided. Finally, it is demonstrated that the smaller values of fractal-fractional order perform better than bigger values for all compartments of the proposed model of HIV/AIDS. We continue to believe that our work will be helpful to researchers working in diverse fields of applied science and engineering. & COPY; 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).