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<p>Hepatitis B virus (HBV) remains a major global health challenge due to its high transmission potential, chronic progression, and significant morbidity. In this study, we formulate and analyze a novel fractional-order compartmental model for Hepatitis B dynamics, incorporating Atangana–Baleanu–Caputo (ABC) derivatives and a Beddington–DeAngelis-type incidence rate. The model accounts for preventive awareness efforts among susceptible individuals, as well as the suppressive impact of treatment on infected populations. Rigorous mathematical analysis is carried out, including the positively invariant region, existence and uniqueness of solutions, equilibrium points, local and global stability, and the computation of the basic reproduction number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({R}_{0}\)</EquationSource> </InlineEquation> using the next-generation matrix approach. Bifurcation analysis reveals the occurrence of a forward bifurcation at <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({R}_{0}=1\)</EquationSource> </InlineEquation>, highlighting the transition from a disease-free state to an endemic state. A sensitivity analysis identifies key parameters influencing <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({R}_{0}\)</EquationSource> </InlineEquation>, particularly the transmission rates from acutely and chronically infected individuals, and the rates of government-led awareness campaigns. Numerical simulations, based on a novel iterative scheme for fractional differential equations, demonstrate the significant role of memory effects in HBV transmission dynamics. Comparative results with the classical integer-order model show that the ABC fractional model more effectively captures the hereditary and long-term memory effects of the disease. The findings suggest that strengthening awareness efforts and improving their effectiveness are as critical as medical interventions in reducing Hepatitis B prevalence. This work provides both theoretical insights and practical guidance for policymakers, offering a comprehensive framework for the control and long-term management of Hepatitis B infection.</p>

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A fractional-order hepatitis B transmission model with Atangana–Baleanu derivative incorporating sociobehavioral and governmental interventions

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  • 发表日期：

    2026年1月6日

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  • Randhir Singh Baghel

摘要

Hepatitis B virus (HBV) remains a major global health challenge due to its high transmission potential, chronic progression, and significant morbidity. In this study, we formulate and analyze a novel fractional-order compartmental model for Hepatitis B dynamics, incorporating Atangana–Baleanu–Caputo (ABC) derivatives and a Beddington–DeAngelis-type incidence rate. The model accounts for preventive awareness efforts among susceptible individuals, as well as the suppressive impact of treatment on infected populations. Rigorous mathematical analysis is carried out, including the positively invariant region, existence and uniqueness of solutions, equilibrium points, local and global stability, and the computation of the basic reproduction number \({R}_{0}\) using the next-generation matrix approach. Bifurcation analysis reveals the occurrence of a forward bifurcation at \({R}_{0}=1\) , highlighting the transition from a disease-free state to an endemic state. A sensitivity analysis identifies key parameters influencing \({R}_{0}\) , particularly the transmission rates from acutely and chronically infected individuals, and the rates of government-led awareness campaigns. Numerical simulations, based on a novel iterative scheme for fractional differential equations, demonstrate the significant role of memory effects in HBV transmission dynamics. Comparative results with the classical integer-order model show that the ABC fractional model more effectively captures the hereditary and long-term memory effects of the disease. The findings suggest that strengthening awareness efforts and improving their effectiveness are as critical as medical interventions in reducing Hepatitis B prevalence. This work provides both theoretical insights and practical guidance for policymakers, offering a comprehensive framework for the control and long-term management of Hepatitis B infection.