Bayesian Spatio–Temporal Outbreak Detection for COVID-19 Mortality in South Africa: A Comparative Study of MCMC and Dynamic HMC Methods

Bayesian Spatio–Temporal Outbreak Detection for COVID-19 Mortality in South Africa: A Comparative Study of MCMC and Dynamic HMC Methods | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Bayesian Spatio–Temporal Outbreak Detection for COVID-19 Mortality in South Africa: A Comparative Study of MCMC and Dynamic HMC Methods Shingirai Artwell Darikwa, Innocent Maposa This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9363716/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract Background: Timely detection of localised COVID-19 surges is essential for targeting limited health resources, yet most routine surveillance algorithms ignore spatial dependence and many Bayesian spatio-temporal models are computationally demanding. Evidence on Hamiltonian Monte Carlo (HMC) performance for outbreak detection in low- and middle-income country (LMIC) settings remains limited. We applied a Bayesian spatio-temporal hidden Markov model (HMM) to South African COVID-19 hospital mortality, comparing data-augmented Markov chain Monte Carlo (MCMC) with dynamic HMC. Methods: We conducted a retrospective ecological time-series study of in-hospital COVID- 19 deaths across 52 districts over 28 months (March 2020–June 2022), using national hospital surveillance linked to district-level health-system and population indicators. Death counts were modelled with a Poisson log-linear specification incorporating a smooth temporal trend, cyclic seasonality, spatial smoothing, and selected covariates, offset by expected deaths from admissions and a case-fatality ratio. Outbreaks were represented by a two-state HMM with latent indicators integrated out analytically and estimated via dynamic HMC in Stan. Eight candidate models were ranked using marginal likelihoods; the preferred model was re-fitted with both samplers to compare runtime, ESS, and convergence. Results: A spatial HMM with marginalised outbreak states was strongly favoured over nonoutbreak and threshold-based alternatives. Posterior outbreak probabilities reproduced the four recognised national waves while revealing marked district-level heterogeneity, with early intense outbreaks in Western Cape and Gauteng districts and later peaks inland. Outbreaks were short-lived (mean around three months), and residual spatial risks indicated persistent excess mortality in the Eastern Cape and Free State. Dynamic HMC and MCMC yielded similar outbreak probability surfaces; however, HMC produced substantially larger ESS 1 (approximately 5,000 versus 63) and near-ideal convergence, whereas MCMC showed poor mixing. ESS per second was similar, so HMC’s extra computation yielded more informative samples. Conclusions: A Bayesian spatio-temporal HMM fitted with dynamic HMC delivers coherent, spatially resolved outbreak probabilities and captures short-lived district-level mortality surges within broader national waves. Despite greater computational intensity, dynamic HMC offers superior mixing and convergence and is preferable for routine surveillance when adequate computing resources are available. The framework is transferable to other routinely collected surveillance data in South Africa and similar LMIC settings. Bayesian outbreak detection Hamiltonian Monte Carlo spatio-temporal modelling COVID-19 South Africa hidden Markov model disease surveillance Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 18 May, 2026 Reviewers agreed at journal 18 May, 2026 Reviewers invited by journal 15 Apr, 2026 Editor invited by journal 13 Apr, 2026 Editor assigned by journal 10 Apr, 2026 Submission checks completed at journal 10 Apr, 2026 First submitted to journal 09 Apr, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9363716","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":626277277,"identity":"c553cb14-5a70-49fa-bb34-5ea61ece65d9","order_by":0,"name":"Shingirai Artwell Darikwa","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/ElEQVRIiWNgGAWjYDACCcYGBgYDZgYGZjYgrwLIJlHLGaK0gEmgFgagFsY2IrTIz25ue/ilwFrevJ0tTeLnvMPy5uzNBxh+VGzDqcXgzsF2YxmDdMM5h9mOSfZuO2y4s+dYAmPPmdu4tUgktklLGBxmnMHM3naDd9thxg03cgyYGdtwa5GfAdFiD9Jy8++cw/YEtTDcSGyT/GBwOHEGM9ux27wNhxMJajEAapFmMEhPBmpJ/y1zLD15w5ljCQfx+UV+RvozyR9/rG1n8B8zNnxTY2274XjzwQc/KvA4DAiYeRDsZjB5AK96IGD8gWDXEVI8CkbBKBgFIxAAADd/WciTUSLXAAAAAElFTkSuQmCC","orcid":"","institution":"Stellenbosch University","correspondingAuthor":true,"prefix":"","firstName":"Shingirai","middleName":"Artwell","lastName":"Darikwa","suffix":""},{"id":626277291,"identity":"ba6dd57a-df40-40a0-b102-31220668fea7","order_by":1,"name":"Innocent Maposa","email":"","orcid":"","institution":"Stellenbosch University","correspondingAuthor":false,"prefix":"","firstName":"Innocent","middleName":"","lastName":"Maposa","suffix":""}],"badges":[],"createdAt":"2026-04-09 05:54:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9363716/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9363716/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107487061,"identity":"1ac98df0-a4dc-414c-ac7f-0ede4294fe9c","added_by":"auto","created_at":"2026-04-22 02:39:45","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1967852,"visible":true,"origin":"","legend":"","description":"","filename":"ManuscriptSourceFile.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9363716/v1_covered_f00d3ea5-3a97-4c33-b8e0-b28e2621d848.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eBayesian Spatio–Temporal Outbreak Detection for COVID-19 Mortality in South Africa: A Comparative Study of MCMC and Dynamic HMC Methods\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"bmc-public-health","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"pubh","sideBox":"Learn more about [BMC Public Health](http://bmcpublichealth.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/pubh/default.aspx","title":"BMC Public Health","twitterHandle":"@BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Bayesian outbreak detection, Hamiltonian Monte Carlo; spatio-temporal modelling, COVID-19, South Africa, hidden Markov model, disease surveillance","lastPublishedDoi":"10.21203/rs.3.rs-9363716/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9363716/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eBackground: Timely detection of localised COVID-19 surges is essential for targeting limited health resources, yet most routine surveillance algorithms ignore spatial dependence and many Bayesian spatio-temporal models are computationally demanding. Evidence on Hamiltonian Monte Carlo (HMC) performance for outbreak detection in low- and middle-income country (LMIC) settings remains limited. We applied a Bayesian spatio-temporal hidden Markov model (HMM) to South African COVID-19 hospital mortality, comparing data-augmented Markov chain Monte Carlo (MCMC) with dynamic HMC.\u003c/p\u003e\n\u003cp\u003eMethods: We conducted a retrospective ecological time-series study of in-hospital COVID- 19 deaths across 52 districts over 28 months (March 2020–June 2022), using national hospital surveillance linked to district-level health-system and population indicators. Death counts were modelled with a Poisson log-linear specification incorporating a smooth temporal trend, cyclic seasonality, spatial smoothing, and selected covariates, offset by expected deaths from admissions and a case-fatality ratio. Outbreaks were represented by a two-state HMM with latent indicators integrated out analytically and estimated via dynamic HMC in Stan. Eight candidate models were ranked using marginal likelihoods; the preferred model was re-fitted with both samplers to compare runtime, ESS, and convergence.\u003c/p\u003e\n\u003cp\u003eResults: A spatial HMM with marginalised outbreak states was strongly favoured over nonoutbreak and threshold-based alternatives. Posterior outbreak probabilities reproduced the four recognised national waves while revealing marked district-level heterogeneity, with early intense outbreaks in Western Cape and Gauteng districts and later peaks inland. Outbreaks were short-lived (mean around three months), and residual spatial risks indicated persistent excess mortality in the Eastern Cape and Free State. Dynamic HMC and MCMC yielded similar outbreak probability surfaces; however, HMC produced substantially larger ESS 1 (approximately 5,000 versus 63) and near-ideal convergence, whereas MCMC showed poor mixing. ESS per second was similar, so HMC’s extra computation yielded more informative samples.\u003c/p\u003e\n\u003cp\u003eConclusions: A Bayesian spatio-temporal HMM fitted with dynamic HMC delivers coherent, spatially resolved outbreak probabilities and captures short-lived district-level mortality surges within broader national waves. Despite greater computational intensity, dynamic HMC offers superior mixing and convergence and is preferable for routine surveillance when adequate computing resources are available. 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