{
  "abstract": "Hepatitis D virus (HDV) infection can substantially worsen the clinical outcomes of individuals infected with hepatitis B virus (HBV), making the prevention of HBV infection and the management of severe HBV–HDV cases important public-health priorities. This study introduces a novel mathematical model for Hepatitis B virus (HBV) and D virus (HDV) transmission, incorporating vaccination and liver transplantation as disease control strategies. In contrast to models that allow direct HDV infection or general coinfection pathways, the proposed model assumes that HDV occurs only through superinfection among individuals already infected with HBV. The model is constructed as a system of ordinary differential equations, where the human population is divided into susceptible, vaccinated, HBV-infected, recovered, chronic, and HDV-infected compartments. Model analysis reveals the existence and stability of the disease-free equilibrium, which exists and is asymptotically stable if the basic reproduction number (ℛ0) is less than one, and becomes unstable if it exceeds one. Two types of endemic equilibria are identified when ℛ0>1, corresponding to the absence and presence of HDV infection. Continuation analysis using MatCont reveals the existence of two branching points that govern the transition of stability between these equilibria, highlighting the conditions under which HDV emerges and persists. Global sensitivity analysis using Partial Rank Correlation Coefficient combined with Latin Hypercube Sampling indicates that vaccination coverage and vaccine efficacy play a dominant role in reducing ℛ0. Although liver transplantation does not affect the magnitude of ℛ0, it significantly influences the disease dynamics by reducing the outbreak size and delaying the timing of HBV and HDV outbreaks. These findings indicate that vaccination is essential for reducing transmission, whereas liver transplantation remains important for mitigating severe disease burden; thus, coordinated use of preventive and clinical interventions is needed for effective HBV–HDV control.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok, Indonesia",
    "Innovative Mathematics and Predictive Analytics for Complex System and Technology Laboratory (IMPACT Lab), Universitas Indonesia, Depok, Indonesia",
    "Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya, Indonesia"
  ],
  "article_type": "Research Article",
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Dipo Aldila"
    },
    {
      "affs": [
        1
      ],
      "name": "Nur Syam Rahman"
    },
    {
      "affs": [
        2
      ],
      "name": "Anymore Majere"
    },
    {
      "name": "Fatmawati"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aw17zkpy8wvaq.bib",
  "cited_by": 0,
  "doi": "10.1371/journal.pone.0356725",
  "fulltext_url": null,
  "id": "aw17zkpy8wvaq",
  "issns": [
    "1932-6203"
  ],
  "landing_url": "https://doi.org/10.1371/journal.pone.0356725",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2739|Mathematical and Theoretical Epidemiology and Ecology Models"
    ],
    [
      "plos",
      "/Biology and life sciences/Immunology/Vaccination and immunization"
    ],
    [
      "plos",
      "/Biology and life sciences/Microbiology/Medical microbiology/Microbial pathogens/Viral pathogens/Hepatitis viruses/Hepatitis B virus"
    ],
    [
      "plos",
      "/Biology and life sciences/Microbiology/Medical microbiology/Microbial pathogens/Viral pathogens/Hepatitis viruses/Hepatitis delta virus"
    ],
    [
      "plos",
      "/Biology and life sciences/Microbiology/Virology/Viral vaccines"
    ],
    [
      "plos",
      "/Biology and life sciences/Organisms/Viruses/Viral pathogens/Hepatitis viruses/Hepatitis B virus"
    ],
    [
      "plos",
      "/Biology and life sciences/Organisms/Viruses/Viral pathogens/Hepatitis viruses/Hepatitis delta virus"
    ],
    [
      "plos",
      "/Biology and life sciences/Population biology/Population metrics/Death rates"
    ],
    [
      "plos",
      "/Medicine and health sciences/Immunology/Vaccination and immunization"
    ],
    [
      "plos",
      "/Medicine and health sciences/Medical conditions/Infectious diseases/Infectious disease control/Vaccines"
    ],
    [
      "plos",
      "/Medicine and health sciences/Medical conditions/Infectious diseases/Infectious disease control/Vaccines/Viral vaccines"
    ],
    [
      "plos",
      "/Medicine and health sciences/Medical conditions/Infectious diseases/Superinfection"
    ],
    [
      "plos",
      "/Medicine and health sciences/Pathology and laboratory medicine/Pathogens/Microbial pathogens/Viral pathogens/Hepatitis viruses/Hepatitis B virus"
    ],
    [
      "plos",
      "/Medicine and health sciences/Pathology and laboratory medicine/Pathogens/Microbial pathogens/Viral pathogens/Hepatitis viruses/Hepatitis delta virus"
    ],
    [
      "plos",
      "/Medicine and health sciences/Public and occupational health/Preventive medicine/Vaccination and immunization"
    ],
    [
      "plos",
      "/Medicine and health sciences/Surgical and invasive medical procedures/Digestive system procedures/Liver transplantation"
    ],
    [
      "plos",
      "/Medicine and health sciences/Surgical and invasive medical procedures/Transplantation/Organ transplantation/Liver transplantation"
    ]
  ],
  "openalex": "W7212001372",
  "pdf_url": "https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0356725&type=printable",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": "Public Library of Science",
  "ris": "https://research.draconitic.com/paper/aw17zkpy8wvaq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:56Z",
      "native_id": "10.1371/journal.pone.0356725",
      "source": "plos",
      "url": "https://doi.org/10.1371/journal.pone.0356725"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "plos:immunology",
      "subfield": "immunology"
    },
    {
      "field": "biology",
      "origin": "plos:microbiology",
      "subfield": "microbiology"
    },
    {
      "field": "medicine",
      "origin": "plos:infectious diseases",
      "subfield": "infectious-disease"
    }
  ],
  "title": "Mathematical modeling of HBV–HDV transmission with superinfection: The role of vaccination and liver transplantation in disease dynamics",
  "title_text": "Mathematical modeling of HBV–HDV transmission with superinfection: The role of vaccination and liver transplantation in disease dynamics",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:56Z",
  "url": "https://research.draconitic.com/paper/aw17zkpy8wvaq",
  "venue": "PLOS One",
  "versions": []
}