Correcting structural bias in dynamical models of infectious disease using a Bayesian state-space framework

Correcting structural bias in dynamical models of infectious disease using a Bayesian state-space framework | 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 Correcting structural bias in dynamical models of infectious disease using a Bayesian state-space framework Miracle Amadi, José Carlos García-Merino, Heikki Haario This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9611525/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Deterministic dynamical models are widely used in infectious disease modelling, but they often become systematically biased when key drivers such as seasonality and random environmental variation are simplified or omitted. This paper proposes a practical way to correct such structural bias without rebuilding the mechanistic model from scratch. We model the observed time series as the sum of (i) a deterministic transmission component given by a reduced Ross malaria model and (ii) a latent stochastic seasonal component that captures unresolved seasonal forcing and other unmodelled variability. The seasonal component is defined as a mean-reverting stochastic differential equation with periodic forcing, which can be interpreted as a seasonally forced Ornstein--Uhlenbeck (OU) process and, at the same time, as a dynamically constrained model-discrepancy term. The combined model forms an additive Bayesian state-space system. A key challenge in additive decompositions is identifiability: many combinations of the deterministic and stochastic components can explain the same observations. We therefore use informative priors to stabilise this decomposition, together with a non-centred parameterisation (a reparameterisation that improves MCMC efficiency by sampling standardised noise terms instead of states directly) of the latent stochastic differential equation (SDE) states that enables efficient joint inference with Hamiltonian Monte Carlo (NUTS) in \texttt{Stan}. We validate the approach in three steps: (1) an OU example that contrasts parameter-only inference with latent state-space inference, (2) synthetic experiments that have a good agreement with the observed signal while highlighting the expected negative posterior dependence between components, and (3) an application to five years of monthly malaria case reports from Delta State, Nigeria. In the real-data analysis, the proposed additive ODE--SDE model produces a close fit with coherent uncertainty quantification and a flexible seasonal reconstruction, while keeping the mechanistic transmission model interpretable. Overall, the framework provides a flexible and transferable method for bias correction in misspecified dynamical models using a structured stochastic discrepancy. Computational Biology malaria transmission dynamical systems stochastic differential equations Bayesian state-space models Hamiltonian Monte Carlo model discrepancy Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted 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. 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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-9611525","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":634358489,"identity":"d1e0ecc6-d4d2-4dba-b574-f2c420415ee7","order_by":0,"name":"Miracle Amadi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1UlEQVRIiWNgGAWjYDACZhBRAGFLJFRYACnGBwcIazGAaTkjwcDDwGyAXwsDshbGNogWvIp123kffvhhYMPAP+3wwxsP50kk7mdgZsRri9lhdmPJHoM0BonbacYWidskEnuAbiWghY1BmsHgMAPD7QQzCYgW/gOEtDD/ZjD4zyB/O/2bROIc4mxhA9pygMHgdg7QlgYitVj2GCTzGN7OKbZIOCZh3HOYkJbzx5hv/Kiwk5O7nb7x5o8aG9n29mbmD/i0wAAPgslMjPpRMApGwSgYBXgBAJFDQn6USV1kAAAAAElFTkSuQmCC","orcid":"","institution":"Lappeenranta-Lahti University of Technology (LUT)","correspondingAuthor":true,"prefix":"","firstName":"Miracle","middleName":"","lastName":"Amadi","suffix":""},{"id":634358780,"identity":"d60c838f-93df-4d58-a7e3-2828dbef78b0","order_by":1,"name":"José Carlos García-Merino","email":"","orcid":"","institution":"Department of Mathematics, School of Technology, 10003, Cáceres (Spain)","correspondingAuthor":false,"prefix":"","firstName":"José","middleName":"Carlos","lastName":"García-Merino","suffix":""},{"id":634358823,"identity":"00de996c-a5e0-4689-82de-9dca1c76e390","order_by":2,"name":"Heikki Haario","email":"","orcid":"","institution":"Lappeenranta-Lahti University of Technology (LUT)","correspondingAuthor":false,"prefix":"","firstName":"Heikki","middleName":"","lastName":"Haario","suffix":""}],"badges":[],"createdAt":"2026-05-04 19:16:04","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9611525/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9611525/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108804403,"identity":"843cb98c-1a5b-47fa-82c8-940b04cd3530","added_by":"auto","created_at":"2026-05-08 15:20:18","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4031889,"visible":true,"origin":"","legend":"","description":"","filename":"ManuscriptBMB.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9611525/v1_covered_e24eb9f0-8469-4663-a6af-352df2f11381.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eCorrecting structural bias in dynamical models of infectious disease using a Bayesian state-space framework\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Lappeenranta University of Technology","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":" malaria transmission, dynamical systems, stochastic differential equations, Bayesian state-space models, Hamiltonian Monte Carlo, model discrepancy","lastPublishedDoi":"10.21203/rs.3.rs-9611525/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9611525/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDeterministic dynamical models are widely used in infectious disease modelling, but they often become systematically biased when key drivers such as seasonality and random environmental variation are simplified or omitted. This paper proposes a practical way to correct such structural bias without rebuilding the mechanistic model from scratch.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWe model the observed time series as the sum of (i) a deterministic transmission component given by a reduced Ross malaria model and (ii) a latent stochastic seasonal component that captures unresolved seasonal forcing and other unmodelled variability. The seasonal component is defined as a mean-reverting stochastic differential equation with periodic forcing, which can be interpreted as a seasonally forced Ornstein--Uhlenbeck (OU) process and, at the same time, as a dynamically constrained model-discrepancy term. The combined model forms an additive Bayesian state-space system.\u003c/p\u003e\n\u003cp\u003eA key challenge in additive decompositions is identifiability: many combinations of the deterministic and stochastic components can explain the same observations. \u0026nbsp;We therefore use informative priors to stabilise this decomposition, together with a non-centred parameterisation (a reparameterisation that improves MCMC efficiency by sampling standardised noise terms instead of states directly) of the latent \u0026nbsp;stochastic differential equation (SDE) states that enables efficient joint inference with Hamiltonian Monte Carlo (NUTS) in \\texttt{Stan}.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWe validate the approach in three steps: (1) an OU example that contrasts parameter-only inference with latent state-space inference, (2) synthetic experiments that have a good agreement with the observed signal while highlighting the expected negative posterior dependence between components, and (3) an application to five years of monthly malaria case reports from Delta State, Nigeria. In the real-data analysis, the proposed additive ODE--SDE model produces a close fit with coherent uncertainty quantification and a flexible seasonal reconstruction, while keeping the mechanistic transmission model interpretable. Overall, the framework provides a flexible and transferable method for bias correction in misspecified dynamical models using a structured stochastic discrepancy.\u003c/p\u003e","manuscriptTitle":"Correcting structural bias in dynamical models of infectious disease using a Bayesian state-space framework","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-06 06:07:09","doi":"10.21203/rs.3.rs-9611525/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"81f7bb4b-dd97-49dd-87e8-b7bc099c8b39","owner":[],"postedDate":"May 6th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":67510488,"name":"Computational Biology"}],"tags":[],"updatedAt":"2026-05-06T06:07:09+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-06 06:07:09","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9611525","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9611525","identity":"rs-9611525","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}