{
  "abstract": "Background: Traditional combined prediction models often face limitations in their ability to capture complex nonlinear relationships and weighting.\n\nObjective: To address these challenges, we propose a nonlinear time-varying weighted combined prediction framework that integrates deep learning algorithms, optimized activation functions, and multifractal theory. This approach results in a robust combined prediction framework.\n\nMethods: The study utilized the weekly total number of influenza cases, the daily number of confirmed cases of COVID-19, and the monthly incidence rates of HIV/AIDS and syphilis as real-world samples. Leveraging mutual information theory, combined prediction models were constructed for influenza and COVID-19 data, employing both linear and time-varying weighting methods. For HIV/AIDS and syphilis data, we applied Empirical Mode Decomposition to decompose the time series, then integrated the decomposed components via linear and time-varying weighting methods. Furthermore, multifractal theory was employed to establish an evaluation framework. The performance of individual models, linear weighted combined models, and activation function-based deep learning combined models were evaluated. This finding provides practical guidance on selecting deep learning approaches and activation functions under nonlinear time-varying weighting framework.\n\nResults: The TCN based on Swish activation function for influenza had the best generalization and accuracy (MAE = 145.391, NMSE = 0.032, IA = 0.992). The LSTM based on Swish activation function had similar generalization and accuracy (MAE = 148.046, NMSE = 0.033, IA = 0.991). The TCN based on Swish activation function for COVID-19 had the best generalization and accuracy (MAE = 25942.744, NMSE = 0.050, IA = 0.986). The LSTM based on ELU activation function for HIV/AIDS exhibited superior predictive performance (MAE = 0.066, NMSE = 0.237, MAPE = 0.081, IA = 0.930). The LSTM based on the adjustment of ELU activation function for syphilis demonstrated superior generalization capability and accuracy (MAE = 0.096, NMSE = 0.215, MAPE = 0.037, IA = 0.931). All of them outperform linear combined prediction models.\n\nConclusions: The proposed nonlinear time-varying weighted combined prediction (NTVWCP) model demonstrates improved predictive accuracy, robustness, and generalization capability compared to traditional models and conventional weighting methods.\n\nGraphical Abstract:\n\nSupplementary Information: The online version contains supplementary material available at https://doi.org/10.1186/s12889-026-28937-2.",
  "abstract_shown": true,
  "affiliations": [
    "Key Lab of Environmental Stress and Chronic Disease Control & Prevention, China Medical University, Shenyang, 110122 PR China",
    "Department of Epidemiology & Health Statistics, School of Public Health, China Medical University, Shenyang, 110122 PR China",
    "Liaoning Provincial Center for Disease Control and Prevention, Shenyang, 110005 PR China",
    "Department of Anesthesiology & Cancer Hospital of China Medical University Liaoning Cancer Hospital & Institute, Shenyang, 110042 PR China",
    "Department of Epidemiology & Health Statistics, Key Lab of Environmental Stress and Chronic Disease Control & Prevention, School of Public Health, China Medical University, No.77 Puhe Road, Shenyang North New Area, Shenyang, Liaoning Province 110122 PR China"
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 8,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "Weijie Cai"
    },
    {
      "affs": [
        0,
        1
      ],
      "name": "Zhi Li"
    },
    {
      "affs": [
        2
      ],
      "name": "Yueya Chu"
    },
    {
      "affs": [
        3
      ],
      "name": "Yi Wang"
    },
    {
      "affs": [
        0,
        1
      ],
      "name": "Xueying Xu"
    },
    {
      "affs": [
        1
      ],
      "name": "Litao Wu"
    },
    {
      "affs": [
        1
      ],
      "name": "Zhouting Yao"
    },
    {
      "affs": [
        0,
        1,
        4
      ],
      "name": "Hongbo Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a334p0pxqk747.bib",
  "cited_by": 0,
  "doi": "10.1186/s12889-026-28937-2",
  "fulltext_url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC13737804/",
  "id": "a334p0pxqk747",
  "issns": [
    "1471-2458"
  ],
  "landing_url": "https://doi.org/10.1186/s12889-026-28937-2",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "heading",
      "Research"
    ],
    [
      "openalex",
      "2713|Data-Driven Disease Surveillance"
    ]
  ],
  "openalex": "W7201971425",
  "pdf_url": null,
  "pmcid": "PMC13737804",
  "pmid": "42983693",
  "published": "2026-08-08",
  "publisher": "BMC",
  "ris": "https://research.draconitic.com/paper/a334p0pxqk747.ris",
  "sources": [
    {
      "first_seen": "2026-11-09T12:22:55Z",
      "native_id": "PMC13737804",
      "source": "pmc",
      "url": "https://doi.org/10.1186/s12889-026-28937-2"
    }
  ],
  "subjects": [
    {
      "field": "medicine",
      "origin": "openalex:2713|Data-Driven Disease Surveillance",
      "subfield": "epidemiology-public-health"
    }
  ],
  "title": "Developing nonlinear time-varying weighted combined prediction framework for infectious diseases: validation with respiratory infectious diseases and sexually transmitted infections",
  "title_text": "Developing nonlinear time-varying weighted combined prediction framework for infectious diseases: validation with respiratory infectious diseases and sexually transmitted infections",
  "type": "peer-reviewed",
  "updated_at": "2026-11-09T12:22:55Z",
  "url": "https://research.draconitic.com/paper/a334p0pxqk747",
  "venue": "BMC Public Health",
  "versions": []
}