{
  "abstract": "The illicit trade in wildlife for pet purposes poses a direct risk to animal populations through overharvesting, but it also serves as an indirect conduit for the spread of contagious diseases. The present study assessed the effects of the hypothetical release of captured, infected individuals of Newcastle disease into the natural population of the white-winged parakeet, the most trafficked psittacine species in Peru. This study analysed the computational dynamical analysis of the stochastic susceptible-exposed-infected-recovered model of Newcastle disease. We take two approaches to stochastic modelling: transition probabilities and the perturbation method. To investigate dynamical features such as positivity, boundedness, consistency, and stability, we introduced a stochastic non-standard finite-difference (SNSFD) scheme. Conventional numerical approaches such as Euler-Maruyama, stochastic Euler, and stochastic Runge–Kutta of order four were applied, but they failed to preserve the system’s essential dynamical properties. Consequently, we formulated the SNSFD method to address this limitation. To support the proposed method, we presented several theorems that demonstrate it satisfies all dynamical properties of the model. In the end, we presented several simulations to compare the proposed method’s efficiency to that of an existing method.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan",
    "Department of Mathematics, Firat University, Elazığ, Türkiye",
    "IT4Innovations, VSB-Technical University of Ostrava, Ostrava, Czech Republic",
    "Research Center of Applied Mathematics, Khazar University, Baku, Azerbaijan",
    "Mathematical Science Department, College of Science, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia"
  ],
  "article_type": "Research Article",
  "arxiv": null,
  "author_total": 6,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Naveed Shahid"
    },
    {
      "affs": [
        1
      ],
      "name": "Ali Raza"
    },
    {
      "affs": [
        2
      ],
      "name": "Marek Lampart"
    },
    {
      "affs": [
        3
      ],
      "name": "Sana Iqbal"
    },
    {
      "affs": [
        4
      ],
      "name": "Nauman Ahmed"
    },
    {
      "name": "Eman Ghareeb Rezk"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/54y36me41bwfx.bib",
  "cited_by": 0,
  "doi": "10.1371/journal.pone.0357918",
  "fulltext_url": null,
  "id": "54y36me41bwfx",
  "issns": [
    "1932-6203"
  ],
  "landing_url": "https://doi.org/10.1371/journal.pone.0357918",
  "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/Microbiology/Medical microbiology/Microbial pathogens/Viral pathogens/Paramyxoviruses/Newcastle disease virus"
    ],
    [
      "plos",
      "/Biology and life sciences/Organisms/Eukaryota/Animals/Vertebrates/Amniotes/Birds"
    ],
    [
      "plos",
      "/Biology and life sciences/Organisms/Eukaryota/Animals/Vertebrates/Amniotes/Birds/Poultry"
    ],
    [
      "plos",
      "/Biology and life sciences/Organisms/Viruses/RNA viruses/Paramyxoviruses/Newcastle disease virus"
    ],
    [
      "plos",
      "/Biology and life sciences/Organisms/Viruses/Viral pathogens/Paramyxoviruses/Newcastle disease virus"
    ],
    [
      "plos",
      "/Biology and life sciences/Population biology/Population metrics/Death rates"
    ],
    [
      "plos",
      "/Biology and life sciences/Veterinary science/Veterinary diseases"
    ],
    [
      "plos",
      "/Biology and life sciences/Zoology/Animals/Vertebrates/Amniotes/Birds"
    ],
    [
      "plos",
      "/Biology and life sciences/Zoology/Animals/Vertebrates/Amniotes/Birds/Poultry"
    ],
    [
      "plos",
      "/Computer and information sciences/Systems science/System stability"
    ],
    [
      "plos",
      "/Medicine and health sciences/Epidemiology/Infectious disease epidemiology"
    ],
    [
      "plos",
      "/Medicine and health sciences/Medical conditions/Infectious diseases/Infectious disease epidemiology"
    ],
    [
      "plos",
      "/Medicine and health sciences/Medical conditions/Infectious diseases/Respiratory infections"
    ],
    [
      "plos",
      "/Medicine and health sciences/Medical conditions/Respiratory disorders/Respiratory infections"
    ],
    [
      "plos",
      "/Medicine and health sciences/Pathology and laboratory medicine/Pathogens/Microbial pathogens/Viral pathogens/Paramyxoviruses/Newcastle disease virus"
    ],
    [
      "plos",
      "/Medicine and health sciences/Pulmonology/Respiratory disorders/Respiratory infections"
    ],
    [
      "plos",
      "/Physical sciences/Mathematics/Systems science/System stability"
    ]
  ],
  "openalex": "W7213454548",
  "pdf_url": "https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0357918&type=printable",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": "Public Library of Science",
  "ris": "https://research.draconitic.com/paper/54y36me41bwfx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:49Z",
      "native_id": "10.1371/journal.pone.0357918",
      "source": "plos",
      "url": "https://doi.org/10.1371/journal.pone.0357918"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "plos:microbiology",
      "subfield": "microbiology"
    },
    {
      "field": "biology",
      "origin": "plos:zoology",
      "subfield": "zoology-behaviour"
    },
    {
      "field": "medicine",
      "origin": "plos:infectious diseases",
      "subfield": "infectious-disease"
    }
  ],
  "title": "Stochastic delay derivatives of Newcastle disease application in epidemic model: Stability analysis and approximation",
  "title_text": "Stochastic delay derivatives of Newcastle disease application in epidemic model: Stability analysis and approximation",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:49Z",
  "url": "https://research.draconitic.com/paper/54y36me41bwfx",
  "venue": "PLOS One",
  "versions": []
}