{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T08:53:38Z","timestamp":1772268818799,"version":"3.50.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1012497","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2024,10,10]],"date-time":"2024-10-10T00:00:00Z","timestamp":1728518400000}}],"reference-count":52,"publisher":"Public Library of Science (PLoS)","issue":"9","license":[{"start":{"date-parts":[[2024,9,30]],"date-time":"2024-09-30T00:00:00Z","timestamp":1727654400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key R&D Program of China","doi-asserted-by":"crossref","award":["2022YFA1003704"],"award-info":[{"award-number":["2022YFA1003704"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Major International (Regional) Joint Research Project of the National Natural Science Foundation of China","award":["12220101001"],"award-info":[{"award-number":["12220101001"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12371502"],"award-info":[{"award-number":["12371502"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12101488"],"award-info":[{"award-number":["12101488"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Young Talent Support Plan of Xi\u2019an Jiaotong University"},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12031010"],"award-info":[{"award-number":["12031010"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Accurate prediction of epidemics is pivotal for making well-informed decisions for the control of infectious diseases, but addressing heterogeneity in the system poses a challenge. In this study, we propose a novel modelling framework integrating the spatio-temporal heterogeneity of susceptible individuals into homogeneous models, by introducing a continuous recruitment process for the susceptibles. A neural network approximates the recruitment rate to develop a Universal Differential Equations (UDE) model. Simultaneously, we pre-set a specific form for the recruitment rate and develop a mechanistic model. Data from a COVID Omicron variant outbreak in Shanghai are used to train the UDE model using deep learning methods and to calibrate the mechanistic model using MCMC methods. Subsequently, we project the attack rate and peak of new infections for the first Omicron wave in China after the adjustment of the dynamic zero-COVID policy. Our projections indicate an attack rate and a peak of new infections of 80.06% and 3.17% of the population, respectively, compared with the homogeneous model\u2019s projections of 99.97% and 32.78%, thus providing an 18.6% improvement in the prediction accuracy based on the actual data. Our simulations demonstrate that heterogeneity in the susceptibles decreases herd immunity for ~37.36% of the population and prolongs the outbreak period from ~30 days to ~70 days, also aligning with the real case. We consider that this study lays the groundwork for the development of a new class of models and new insights for modelling heterogeneity.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1012497","type":"journal-article","created":{"date-parts":[[2024,9,30]],"date-time":"2024-09-30T17:39:07Z","timestamp":1727717947000},"page":"e1012497","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":4,"title":["Managing spatio-temporal heterogeneity of susceptibles by embedding it into an homogeneous model: A mechanistic and deep learning study"],"prefix":"10.1371","volume":"20","author":[{"given":"Biao","family":"Tang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kexin","family":"Ma","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9317-4824","authenticated-orcid":true,"given":"Xia","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sanyi","family":"Tang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanni","family":"Xiao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7437-1934","authenticated-orcid":true,"given":"Robert A.","family":"Cheke","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2024,9,30]]},"reference":[{"key":"pcbi.1012497.ref001","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1038\/s41591-021-01301-0","article-title":"Vaccine development for emerging infectious diseases","volume":"27","author":"J-L Excler","year":"2021","journal-title":"Nat Med"},{"key":"pcbi.1012497.ref002","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1038\/s41579-021-00639-z","article-title":"Infectious disease in an era of global change","volume":"20","author":"RE Baker","year":"2022","journal-title":"Nat Rev Microbiol"},{"key":"pcbi.1012497.ref003","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1056\/NEJMra1108296","article-title":"The perpetual challenge of infectious diseases","volume":"366","author":"AS Fauci","year":"2012","journal-title":"N Engl J Med"},{"key":"pcbi.1012497.ref004","doi-asserted-by":"crossref","first-page":"1474","DOI":"10.1001\/jama.292.12.1474","article-title":"International efforts to control infectious diseases, 1851 to the present","volume":"292","author":"AM Stern","year":"2004","journal-title":"JAMA"},{"key":"pcbi.1012497.ref005","doi-asserted-by":"crossref","first-page":"e488","DOI":"10.1016\/S2214-109X(20)30074-7","article-title":"Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts","volume":"8","author":"J Hellewell","year":"2020","journal-title":"The Lancet Global Health"},{"key":"pcbi.1012497.ref006","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/S1473-3099(05)70325-X","article-title":"Mathematical modelling: a tool for hospital infection control","volume":"6","author":"H Grundmann","year":"2006","journal-title":"The Lancet Infectious Diseases"},{"key":"pcbi.1012497.ref007","doi-asserted-by":"crossref","first-page":"aaa4339","DOI":"10.1126\/science.aaa4339","article-title":"Modeling infectious disease dynamics in the complex landscape of global health","volume":"347","author":"H Heesterbeek","year":"2015","journal-title":"Science"},{"key":"pcbi.1012497.ref008","doi-asserted-by":"crossref","first-page":"100679","DOI":"10.1016\/j.epidem.2023.100679","article-title":"Accounting for historical injustices in mathematical models of infectious disease transmission: an analytic overview","volume":"43","author":"NN Abuelezam","year":"2023","journal-title":"Epidemics"},{"key":"pcbi.1012497.ref009","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/S0169-5347(01)02144-9","article-title":"How should pathogen transmission be modelled?","volume":"16","author":"H. 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