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The infection-rate is dependent on population mixing patterns that do not vary erratically day-to-day; in contrast, daily case-counts used in contemporary surveillance algorithms are corrupted by reporting errors. The technical challenge lies in estimating the latent infection-rate from case-counts. Here we devise a Bayesian method to estimate the infection-rate across multiple adjoining areal units, and then use it, via an anomaly detector, to discern a change in epidemiological dynamics. We extend an existing model for estimating the infection-rate in an areal unit by incorporating a Markov random field model, so that we may estimate infection-rates across multiple areal units, while preserving spatial correlations observed in the epidemiological dynamics. To carry out the high-dimensional Bayesian inverse problem, we develop an implementation of mean-field variational inference specific to the infection model and integrate it with the random field model to incorporate correlations across counties. The method is tested on estimating the COVID-19 infection-rates across all 33 counties in New Mexico using data from the summer of 2020, and then employing them to detect the arrival of the Fall 2020 COVID-19 wave. We perform the detection using a temporal algorithm that is applied county-by-county. We also show how the infection-rate field can be used to cluster counties with similar epidemiological dynamics.<\/jats:p>","DOI":"10.1371\/journal.pone.0350090","type":"journal-article","created":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T17:33:35Z","timestamp":1780076015000},"page":"e0350090","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["A scalable variational method for estimating the latent infection-rate field of an outbreak"],"prefix":"10.1371","volume":"21","author":[{"given":"Wyatt H.","family":"Bridgman","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cosmin","family":"Safta","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-9908-7035","authenticated-orcid":true,"given":"Jaideep","family":"Ray","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2026,5,29]]},"reference":[{"key":"pone.0350090.ref001","doi-asserted-by":"crossref","first-page":"100564","DOI":"10.1016\/j.epidem.2022.100564","article-title":"Bayesian sequential data assimilation for COVID-19 forecasting","volume":"39","author":"ML Daza-Torres","year":"2022","journal-title":"Epidemics"},{"issue":"5","key":"pone.0350090.ref002","doi-asserted-by":"crossref","first-page":"1153","DOI":"10.1007\/s00466-020-01894-2","article-title":"System inference for the spatio-temporal evolution of infectious diseases: Michigan in the time of COVID-19","volume":"66","author":"Z Wang","year":"2020","journal-title":"Comput Mech"},{"key":"pone.0350090.ref003","doi-asserted-by":"crossref","first-page":"114020","DOI":"10.1016\/j.cma.2021.114020","article-title":"Bayesian inference of heterogeneous epidemic models: Application to COVID-19 spread accounting for long-term care facilities","volume":"385","author":"P Chen","year":"2021","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"6","key":"pone.0350090.ref004","doi-asserted-by":"crossref","first-page":"4169","DOI":"10.1007\/s11831-021-09603-9","article-title":"Forecasting Multi-Wave Epidemics Through Bayesian Inference","volume":"28","author":"P Blonigan","year":"2021","journal-title":"Arch Comput Methods Eng"},{"issue":"3","key":"pone.0350090.ref005","doi-asserted-by":"crossref","first-page":"767","DOI":"10.3201\/eid2703.203364","article-title":"Daily Forecasting of Regional Epidemics of Coronavirus Disease with Bayesian Uncertainty Quantification, United States","volume":"27","author":"YT Lin","year":"2021","journal-title":"Emerg Infect Dis"},{"issue":"5","key":"pone.0350090.ref006","doi-asserted-by":"crossref","first-page":"1109","DOI":"10.1007\/s00466-020-01897-z","article-title":"Characterization of partially observed epidemics through Bayesian inference: application to COVID-19","volume":"66","author":"C Safta","year":"2020","journal-title":"Comput Mech"},{"issue":"2","key":"pone.0350090.ref007","doi-asserted-by":"crossref","first-page":"223","DOI":"10.2307\/3318737","article-title":"An Adaptive Metropolis Algorithm","volume":"7","author":"H Haario","year":"2001","journal-title":"Bernoulli"},{"key":"pone.0350090.ref008","unstructured":"Safta C, Bridgman W, Ray J. 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