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<p>Measles is a highly contagious and potentially fatal viral disease that spreads primarily through direct contact with infected individuals. In this study, we develop a fractional measles infection model using the Atangana-Baleanu fractional derivative with a nonlocal and non-singular kernel. To analyze the considered model, we apply the generalized Euler method (GEM), a semi-analytical numerical approach tailored for fractional-order nonlinear systems of ordinary differential equations (ODEs). The proposed method approximates solutions as a series of polynomials, ensuring both accuracy and stability through iterative computations. We also examine the uniqueness and convergence of the obtained solutions using fixed-point theory. In addition, the model equilibria are determined, and the novel Jacobian determinant method recently constructed in the literature of epidemiological modeling of infectious diseases is applied to determine the threshold quantity, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {R_0}\)</EquationSource> </InlineEquation>. Furthermore, we construct appropriate Lyapunov functions to establish the global asymptotic stability of the disease-free and endemic equilibrium points. Numerical simulations are carried out in MATLAB 2021a for various integer and non-integer orders within the interval (0, 1] along with sensitivity analysis of key model parameters. The simulation results demonstrate that interventions such as quarantine, vaccination, and treatment significantly reduce the exposed and infectious populations, thereby contributing to effective disease control. Based on these findings, we recommend that governments allocate financial support to enhance vaccine distribution programs.</p>

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Generalized Euler method to study the vaccination effects on dynamics of measles infection model under non-singular kernel

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月25日

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  • L. K. Yadav,
  • M. M. Gour,
  • S. D. Purohit,
  • Qasem Al-Mdallal,
  • D. L. Suthar

摘要

Measles is a highly contagious and potentially fatal viral disease that spreads primarily through direct contact with infected individuals. In this study, we develop a fractional measles infection model using the Atangana-Baleanu fractional derivative with a nonlocal and non-singular kernel. To analyze the considered model, we apply the generalized Euler method (GEM), a semi-analytical numerical approach tailored for fractional-order nonlinear systems of ordinary differential equations (ODEs). The proposed method approximates solutions as a series of polynomials, ensuring both accuracy and stability through iterative computations. We also examine the uniqueness and convergence of the obtained solutions using fixed-point theory. In addition, the model equilibria are determined, and the novel Jacobian determinant method recently constructed in the literature of epidemiological modeling of infectious diseases is applied to determine the threshold quantity, \(\mathcal {R_0}\) . Furthermore, we construct appropriate Lyapunov functions to establish the global asymptotic stability of the disease-free and endemic equilibrium points. Numerical simulations are carried out in MATLAB 2021a for various integer and non-integer orders within the interval (0, 1] along with sensitivity analysis of key model parameters. The simulation results demonstrate that interventions such as quarantine, vaccination, and treatment significantly reduce the exposed and infectious populations, thereby contributing to effective disease control. Based on these findings, we recommend that governments allocate financial support to enhance vaccine distribution programs.