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  • Küçük Resim
    Öğe
    Dynamical analysis of fractional hepatitis B model with Gaussian uncertainties using extended residual power series algorithm
    (Springer Science and Business Media LLC, 2025-03-07) Qursam Fatima; Mubashir Qayyum; Murad Khan Hassani; Ali Akgül
    Hepatitis B virus (HBV) is a significant global health concern, causing acute and chronic liver diseases, including cirrhosis and hepatocellular carcinoma. This manuscript extends existing mathematical models for HBV by introducing a treatment compartment to improve understanding, diagnosis, and treatment strategies. A stability analysis is conducted for disease-free equilibrium and to address the inherent uncertainties in parameter values, Gaussian fuzzy numbers are incorporated, resulting in a more realistic predictive framework. For solution purposes, the extended residual power series algorithm, which combines the Taylor series with a residual function and an integral transform, is applied. The accuracy of the obtained solutions is assessed by calculating the associated errors. The robustness of the model is further evaluated using r-cut values for lower and upper bounds.A graphical analysis is also performed to examine the influence of different parameters on the solution profiles, enhancing the understanding of disease dynamics. The analysis reveals that the proposed methodology effectively explains the dynamics of epidemic systems and provides new perspectives with potential applications in biology, engineering, and medicine.
  • Küçük Resim
    Öğe
    Modeling and analysis of dengue transmission in fuzzy-fractional framework: a hybrid residual power series approach
    (Springer Science and Business Media LLC, 2024-12-28) Mubashir Qayyum; Qursam Fatima; Ali Akgül; Murad Khan Hassani
    The current manuscript presents a mathematical model of dengue fever transmission with an asymptomatic compartment to capture infection dynamics in the presence of uncertainty. The model is fuzzified using triangular fuzzy numbers (TFNs) approach. The obtained fuzzy-fractional dengue model is then solved and analyzed through fuzzy extension of modified residual power series algorithm, which utilizes residual power series along with Laplace transform. Numerical analysis has also been performed in this study and obtained results are shown as solutions and residual errors for each compartment to ensure the validity. Graphical analysis depict the model’s behavior under varying parameters, illustrating contrasting trends for different values of and examining the impacts of transmission and recovery rates on dengue model in uncertain environment. The current findings highlighted the effectiveness of proposed uncertainty in epidemic system dynamics, offering new insights with potential applications in other areas of engineering, science and medicine.