From Transmission to Disability: A Fractional Perspective on HBV Dynamics

Moving beyond classical epidemiological models, this work explores how infectious disease dynamics can be linked to long-term disability outcomes.
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BioMed Central
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Fractional modeling of hepatitis B virus transmission via heterosexual and homosexual contacts and its disability burden - BMC Infectious Diseases

The hepatitis B virus (HBV) is a major public health problem worldwide. Sexual intercourse, heterosexual and homosexual, is an important factor in HBV transmission in adults. This study develops a fractional-order mathematical model to describe the spread of HBV, using fractional calculus with a Mittag–Leffler kernel to account for memory effects and hereditary properties of biological systems. The adult population is divided into the groups of susceptible, infected, carrier, and recovered, on the basis of sex and sexual habits. The model incorporates HBV-related disability using gender-specific probabilities that capture long-term functional impairments among carriers. We derive the basic reproduction number (R0) and analyze the disease-free equilibrium (E0). Theoretical results include conditions ensuring existence and uniqueness of solutions and the Hyers–Ulam stability of the system. Sensitivity analysis of R0 identifies infection rates among same-sex partners, contact frequency, and immunity levels as major factors influencing HBV dynamics. Numerical simulations based on the generalized Mittag–Leffler kernel illustrate the model’s behavior over time. The findings suggest that strengthening immunization programs, reducing the number of carriers, and promoting safe sexual practices can effectively control HBV transmission. The study highlights the value of fractional-order models for capturing complex disease processes and evaluating long-term health outcomes within affected populations.

What if infectious disease models systematically underestimate long-term human suffering?

Infectious disease modeling should not stop at transmission dynamics. It must also capture the long-term health consequences that shape real-world impact.

In our recent study published in BMC Infectious Diseases, we developed a fractional-order mathematical framework to model hepatitis B virus transmission across heterogeneous contact structures while explicitly incorporating disability burden into the system.

Unlike classical integer-order approaches, the model integrates memory effects using a Mittag–Leffler kernel, enabling a more realistic representation of disease progression and persistence over time.

A key contribution of this work is the introduction of disability-aware parameters that quantify long-term functional impairment among infected individuals. By incorporating metrics such as Years Lived with Disability and Disability-Adjusted Life Years, the model connects epidemiological dynamics with measurable health outcomes.

Through analytical and numerical investigations, including reproduction number analysis and sensitivity assessment, the results highlight the critical role of vaccination, transmission behavior, and carrier dynamics in shaping both infection spread and long-term disability burden.

This work contributes to a growing research direction that integrates mathematical modeling, artificial intelligence, and public health to support predictive, data-driven healthcare strategies.

https://doi.org/10.1186/s12879-025-12117-5

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Infectious Diseases
Life Sciences > Biological Sciences > Microbiology > Medical Microbiology > Infectious Diseases
Artificial Intelligence
Mathematics and Computing > Computer Science > Artificial Intelligence
Epidemiology
Life Sciences > Health Sciences > Biomedical Research > Epidemiology

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