Mathematical and Dynamical Analysis of Hepatitis B Model with Hybrid Operator Piecewise Classical and Fractional Derivative Insight of Different Stages of Vaccinations

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DOI: https://doi.org/10.28924/2291-8639-24-2026-241
Published: Aug 3, 2026
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Muhammad Farman, Kottakkaran Sooppy Nisar, Mathematical and Dynamical Analysis of Hepatitis B Model with Hybrid Operator Piecewise Classical and Fractional Derivative Insight of Different Stages of Vaccinations, Int. J. Anal. Appl., 24 (2026), 241.

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Muhammad Farman, Kottakkaran Sooppy Nisar

Abstract

In order to observe the dynamics and impacts of vaccination at different phases, we suggested an epidemic model in this paper that includes classical and Atangana-Baleanu piecewise operators for the hybrid operator’s memory effects. The created model’s properties, which take into account linear growth and Lipschitz requirements relating the rate of effects within its many sub-compartments according to the equilibrium points, include positivity, unique solution, existence, and boundedness in the feasible domain. The reproductive number \(R_0\) is derived for the biological feasibility of the model with sensitivity analysis with different parameters impacting the model for the piecewise fractional operator. Global stability employs Lyapunov function theory to gain insight into first derivative results. The chaotic behavior of the system was also determined through simulation, which shows the solution is bound to a steady state point and lies in a feasible region.For numerical solutions, classical and piecewise fractional hybrid operators at various fractional order values are solved using the Newton polynomial interpolation method.This research advances our knowledge of the dynamics of hepatitis B and offers a solid framework for assessing the effectiveness of interventions for disease control planning and decision-making.

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