{
  "abstract": "We extend the delayed reaction–diffusion SI model with nonlinear incidence proposed by Song et al. by replacing the fixed transmission lag with weak and strong gamma-distributed memory kernels. Because the model has no exposed compartment, the memory term is interpreted phenomenologically as a distributed timing of transmission-related effects of past infectious states rather than as an explicit latent-stage mechanism. Using the same parameter set adopted by Song et al., we show that the distributed-memory models have a stability structure that is qualitatively different from that of the discrete-delay model. For the spatially homogeneous mode, both gamma kernels exhibit a small stabilising spectral Hopf crossing at a mean memory time near 0.08. The discrete-delay model has a comparable small stabilising crossing but, in addition, a much larger destabilising crossing near τ=1.335. Consequently, at the nominal values 1.2 and 1.6 used in the reference simulations, the gamma models converge to the selected endemic equilibrium, whereas the discrete-delay model crosses into an oscillatory regime. The first spatial mode is different: for the gamma formulations its modal constant term is negative for every positive memory rate, so this mode is unstable for every positive mean-memory value. We therefore interpret this behavior as a memory-independent spatial-mode instability, distinct from both a memory-induced Hopf crossing and a classical Turing instability.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, University of Cape Coast, Cape Coast, Ghana",
    "Department of Management, Polytechnic University of Marche, Ancona, Italy",
    "Department of Computer Science, Sunyani Technical University, Sunyani, Ghana",
    "Department of Statistical Sciences, Kumasi Technical University, Kumasi, Ghana",
    "Department of Economics and Management, University of Ferrara, Ferrara, Italy"
  ],
  "article_type": "Research Article",
  "arxiv": null,
  "author_total": 5,
  "authors": [
    {
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        0
      ],
      "name": "Martin Anokye"
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    {
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        1
      ],
      "name": "Luca Guerrini"
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    {
      "affs": [
        2
      ],
      "name": "John Amoah Mensah"
    },
    {
      "affs": [
        3
      ],
      "name": "Michael Fosu Ofori"
    },
    {
      "affs": [
        4
      ],
      "name": "Stefania Ragni"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3dhqx1n4e0m18.bib",
  "cited_by": 0,
  "doi": "10.1371/journal.pone.0360508",
  "fulltext_url": null,
  "id": "3dhqx1n4e0m18",
  "issns": [
    "1932-6203"
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  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "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/Computational biology/Population modeling/Infectious disease modeling"
    ],
    [
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      "/Biology and life sciences/Population biology/Population modeling/Infectious disease modeling"
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      "plos",
      "/Computer and information sciences/Systems science/Nonlinear dynamics"
    ],
    [
      "plos",
      "/Medicine and health sciences/Epidemiology"
    ],
    [
      "plos",
      "/Medicine and health sciences/Epidemiology/Spatial epidemiology"
    ],
    [
      "plos",
      "/Medicine and health sciences/Medical conditions/Infectious diseases/Infectious disease modeling"
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      "plos",
      "/Physical sciences/Mathematics/Systems science/Nonlinear dynamics"
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      "/Research and analysis methods/Mathematical and statistical techniques/Mathematical functions/Transfer functions"
    ],
    [
      "plos",
      "/Research and analysis methods/Simulation and modeling"
    ],
    [
      "plos",
      "/Research and analysis methods/Spectrum analysis techniques/Gamma spectrometry"
    ]
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  "openalex": "W7221814494",
  "pdf_url": "https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0360508&type=printable",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": "Public Library of Science",
  "ris": "https://research.draconitic.com/paper/3dhqx1n4e0m18.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:23Z",
      "native_id": "10.1371/journal.pone.0360508",
      "source": "plos",
      "url": "https://doi.org/10.1371/journal.pone.0360508"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "plos:computational biology",
      "subfield": "bioinformatics"
    },
    {
      "field": "medicine",
      "origin": "plos:epidemiology",
      "subfield": "epidemiology-public-health"
    },
    {
      "field": "medicine",
      "origin": "plos:infectious diseases",
      "subfield": "infectious-disease"
    }
  ],
  "title": "Gamma–distributed transmission memory in a reaction–diffusion epidemic model with nonlinear incidence",
  "title_text": "Gamma–distributed transmission memory in a reaction–diffusion epidemic model with nonlinear incidence",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:23Z",
  "url": "https://research.draconitic.com/paper/3dhqx1n4e0m18",
  "venue": "PLOS One",
  "versions": []
}