{
  "abstract": "We study long-run optimal intervention strategies for endemic infections in a stochastic susceptible-infected-susceptible (SIS) model. The proportion of infected individuals evolves as a diffusion process with random fluctuations, while a control variable $ζ_t\\in[0,\\tildeζ_{max}]$ represents the intensity of public health interventions that reduce transmission for some intervention threshold $\\tildeζ_{max}\\in (0,1]$. The objective is to minimize the long-run average societal cost, balancing the burden of infection against the costs of interventions. Under a concave intervention cost structure the problem can be formulated as an ergodic stochastic control problem, whose structure implies (under certain additional conditions) that optimal interventions are of bang-bang type, switching between no intervention and the maximal admissible intervention at a single switching threshold in the infection level. We construct candidate value functions, rigorously verify optimality in this single-threshold case, and relate the results to extinction and persistence properties of the underlying SIS dynamics in the absence of control. In our framework, the analysis provides a rigorous justification for the threshold-based intervention rules commonly used in epidemic management.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05495",
  "author_total": 4,
  "authors": [
    {
      "name": "Matthew Buckland"
    },
    {
      "name": "Sören Christensen"
    },
    {
      "name": "Philip Le Borne"
    },
    {
      "name": "Cornelia Pokalyuk"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8g3jtsrctqh16.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05495",
  "fulltext_url": null,
  "id": "8g3jtsrctqh16",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05495",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "q-bio.PE"
    ],
    [
      "openalex",
      "2739|Mathematical and Theoretical Epidemiology and Ecology Models"
    ]
  ],
  "openalex": "W7212044286",
  "pdf_url": "https://arxiv.org/pdf/2609.05495",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8g3jtsrctqh16.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.05495",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05495"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.PE",
      "subfield": "evolutionary-biology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Optimal long-run control of endemic infections: bang-bang threshold policies in a stochastic SIS model",
  "title_text": "Optimal long-run control of endemic infections: bang-bang threshold policies in a stochastic SIS model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:02Z",
  "url": "https://research.draconitic.com/paper/8g3jtsrctqh16",
  "venue": "arXiv",
  "versions": []
}