{
  "abstract": "A delayed malware dissemination model for wireless sensor networks is extended by replacing the single fixed anti-virus cycle time with distributed recovery memories. Two normalized gamma kernels are considered: a one-stage exponential memory (weak kernel) and a two-stage gamma memory (strong kernel), both representing heterogeneous anti-virus removal times across carrier and infectious nodes. The linear chain trick transforms the corresponding integro-differential systems into six- and eight-dimensional ordinary differential equation models. For these distributed-delay formulations, we derive the common disease-free equilibrium and its local stability conditions, prove that the endemic equilibrium and the basic reproduction number are preserved, and show that the inherited delayed-removal mechanism does not generate a positively invariant nonnegative orthant; in its place, we establish the strongest valid conditional boundedness and continuation result. Local endemic stability is reduced to a Routh–Hurwitz problem, and Hopf thresholds are obtained from simple purely imaginary roots together with transversality. For the reference parameter set, full spectral verification and first-Lyapunov-coefficient evaluation show that the first weak- and strong-kernel Hopf points are subcritical. Numerical simulations illustrate convergence below threshold and loss of equilibrium stability above it, while comparison with the discrete-delay benchmark shows that a broader recovery-time distribution postpones instability.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Carlo Bianca"
    },
    {
      "name": "Luca Guerrini"
    },
    {
      "name": "Stefania Ragni"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9tfqs092bx2h3.bib",
  "cited_by": 0,
  "doi": "10.3390/appliedmath6090144",
  "fulltext_url": null,
  "id": "9tfqs092bx2h3",
  "issns": [
    "2673-9909"
  ],
  "landing_url": "https://hal.science/hal-05770873v1",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "2739|Mathematical and Theoretical Epidemiology and Ecology Models"
    ]
  ],
  "openalex": "W7208795670",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": "MDPI",
  "ris": "https://research.draconitic.com/paper/9tfqs092bx2h3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:44Z",
      "native_id": "hal-05770873",
      "source": "hal",
      "url": "https://hal.science/hal-05770873v1"
    }
  ],
  "subjects": [
    {
      "field": "medicine",
      "origin": "openalex:2739|Mathematical and Theoretical Epidemiology and Ecology Models",
      "subfield": "epidemiology-public-health"
    }
  ],
  "title": "Stability and Hopf Criteria in a Malware Dissemination Model for Wireless Sensor Networks with Distributed Recovery Delays",
  "title_text": "Stability and Hopf Criteria in a Malware Dissemination Model for Wireless Sensor Networks with Distributed Recovery Delays",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:44Z",
  "url": "https://research.draconitic.com/paper/9tfqs092bx2h3",
  "venue": "AppliedMath",
  "versions": []
}