{
  "abstract": "A Liouville-based framework is developed for optimizing treatment strategies in oesophageal cancer (OC) while accounting for inter-patient heterogeneity. Variability within a patient cohort is represented through uncertain initial cancer and immune cell populations, whose probability distribution is propagated by a Liouville partial differential equation while the underlying individual dynamics remains deterministic. Two optimization problems are considered. First, model parameters are estimated from population-level data using an adjoint-based projected nonlinear conjugate-gradient (NCG) method. Second, optimal time-dependent combinations of chemotherapy and immunotherapy are determined using a sequential quadratic Hamiltonian (SQH) scheme based on Pontryagin’s maximum principle (PMP). The Liouville equation is discretized using a finite-volume method designed to preserve positivity and conservation of the probability density. Numerical experiments with synthetic population data are used to demonstrate the parameter-estimation framework and the ability of the proposed optimal control strategy to determine treatment protocols that effectively modify the population-level cancer–immune response while limiting treatment exposure.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, The University of Texas at Arlington 1 , Arlington, TX, USA",
    "Majmaah University 2 , Al Majmaah, Riyadh Province, Saudi Arabia",
    "Najran University 3 , Najran, Najran Province, Saudi Arabia",
    "University of Tabouk 4 , Tabuk, Tabuk Province, Saudi Arabia",
    "UT Southwestern Medical Center 5 , Dallas, TX, USA",
    "University of Maryland College Park 6 , College Park, MD, USA"
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 11,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Souvik Roy",
      "orcid": "0000-0002-6134-1381"
    },
    {
      "affs": [
        1
      ],
      "name": "Naif Abu Qarnayn"
    },
    {
      "affs": [
        2
      ],
      "name": "Mesfer H. F. Alajmi",
      "orcid": "0009-0007-9010-2332"
    },
    {
      "affs": [
        3
      ],
      "name": "Asma Alghamdi"
    },
    {
      "affs": [
        3
      ],
      "name": "Ibrahem Alshaoosh"
    },
    {
      "affs": [
        4
      ],
      "name": "Shreshtha Chaturvedi"
    },
    {
      "affs": [
        0
      ],
      "name": "Olusola Dehinsilu"
    },
    {
      "affs": [
        0
      ],
      "name": "Rodina El-Adawy"
    },
    {
      "affs": [
        5
      ],
      "name": "Darsh Gandhi"
    },
    {
      "affs": [
        0
      ],
      "name": "DeAnna Patterson"
    },
    {
      "affs": [
        0
      ],
      "name": "Jordan Rodriguez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0hmxktb7q7dqw.bib",
  "cited_by": 0,
  "doi": "10.1098/rsos.261866",
  "fulltext_url": "https://europepmc.org/articles/PMC13714371",
  "id": "0hmxktb7q7dqw",
  "issns": [
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  "landing_url": "https://royalsocietypublishing.org/rsos/article/13/10/261866/483957/A-Liouville-dynamical-modelling-and-control",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "metadata_licence": null,
  "native_subjects": [
    [
      "heading",
      "Applied Mathematics"
    ],
    [
      "heading",
      "Biomathematics"
    ],
    [
      "heading",
      "Mathematical Modelling"
    ],
    [
      "heading",
      "Mathematics"
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  "pdf_url": "https://royalsocietypublishing.org/rsos/article-pdf/doi/10.1098/rsos.261866/6174421/rsos.261866.pdf",
  "pmcid": "PMC13714371",
  "pmid": "42953350",
  "published": "2026-10-07",
  "publisher": "The Royal Society",
  "ris": "https://research.draconitic.com/paper/0hmxktb7q7dqw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:45Z",
      "native_id": "10.1098/rsos.261866",
      "source": "crossref",
      "url": "https://royalsocietypublishing.org/rsos/article/13/10/261866/483957/A-Liouville-dynamical-modelling-and-control"
    },
    {
      "first_seen": "2026-10-31T00:20:40Z",
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "heading:Mathematics",
      "subfield": "general"
    }
  ],
  "title": "A Liouville dynamical modelling and control framework for oesophageal cancer-induced immune response",
  "title_text": "A Liouville dynamical modelling and control framework for oesophageal cancer-induced immune response",
  "type": "peer-reviewed",
  "updated_at": "2026-11-01T12:21:53Z",
  "url": "https://research.draconitic.com/paper/0hmxktb7q7dqw",
  "venue": "Royal Society Open Science",
  "versions": []
}