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  "title": "Reconstruction and continuation in network SIS epidemics",
  "shortTitle": "What the past can—and cannot—predict",
  "url": "https://evidencepress.org/releases/sis-reconstruction-continuation/",
  "oneLine": "Fixed-size network SIS models admit linear continuation, growing networks do not admit one dimension-free linear factor, and an explicit Hölder bound restores uniform control.",
  "abstract": "Keliger and Horváth asked whether an observable fitting residual for the deterministic susceptible–infected–susceptible network model admits a uniform continuation factor, first at fixed dimension and then over all network sizes. This candidate proves the fixed-dimensional assertion and disproves the dimension-free linear assertion using exactly reconstructible complete weighted networks with exponential amplification. It supplies an explicit dimension-free Hölder replacement, extends it directly to full community-resolved trajectory error, and proves a deterministic finite-sampling corollary with fill-distance and bounded measurement-error terms. It also characterises reconstruction fibres, gives nonstationary counterexamples to a proposed block-regularity characterisation, and classifies positive invariant rays. The estimates are for the stated deterministic model and norms; the exponent is not claimed optimal or practically sharp. AI-assisted, unrefereed candidate; no external peer review, independent reproduction or formal verification is claimed.",
  "datePublished": "2026-10-21",
  "dateModified": "2026-10-21",
  "version": "1.0.1-candidate",
  "doi": "10.5281/zenodo.23525167",
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  "authors": [
    "Anonymous"
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  "status": "unrefereed-candidate",
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  "keywords": [
    "network epidemiology",
    "SIS model",
    "inverse problems",
    "analytic continuation",
    "reconstruction",
    "Hölder stability"
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    "For every fixed network dimension and bounded SIS parameter class, the least interval-continuation factor is uniformly finite (analytic proof).",
    "An exactly reconstructible bounded SIS family has least continuation factors growing at least exponentially with the number of communities, so no dimension-free linear factor exists.",
    "An explicit dimension-free Hölder continuation estimate controls both the residual and differences between full community-resolved trajectories.",
    "A deterministic corollary converts finite community-resolved samples into continuation control using fill distance η and bounded sample error σ.",
    "The symmetric contact-matrix ambiguity space has dimension (n−r)(n−r+1)/2 when the trajectory span has dimension r; positive invariant rays are classified."
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  "relatedWorks": [
    {
      "citation": "Keliger and Horváth (2026), Reconstruction of the network in the N-intertwined mean-field approximation of the SIS epidemic model.",
      "url": "https://doi.org/10.1007/s11538-026-01550-7",
      "doi": "10.1007/s11538-026-01550-7"
    },
    {
      "citation": "Trefethen (2020), Quantifying the ill-conditioning of analytic continuation.",
      "url": "https://doi.org/10.1007/s10543-020-00802-7",
      "doi": "10.1007/s10543-020-00802-7"
    },
    {
      "citation": "Prasse, Devriendt and Van Mieghem (2021), Clustering for epidemics on networks: A geometric approach.",
      "url": "https://doi.org/10.1063/5.0048779",
      "doi": "10.1063/5.0048779"
    }
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