Multi-Patch Epidemic Models with General Exposed and Infectious Periods

Simple item page
dc.citation.firstpage345en_US
dc.citation.journalTitleESAIM: Probability and Statisticsen_US
dc.citation.lastpage401en_US
dc.citation.volumeNumber27en_US
dc.contributor.authorPang, Guodongen_US
dc.contributor.authorPardoux, Étienneen_US
dc.date.accessioned2023-03-23T14:10:38Zen_US
dc.date.available2023-03-23T14:10:38Zen_US
dc.date.issued2023en_US
dc.description.abstractWe study multi-patch epidemic models where individuals may migrate from one patch to another in either of the susceptible, exposed/latent, infectious and recovered states. We assume that infections occur both locally with a rate that depends on the patch as well as “from distance” from all the other patches. The migration processes among the patches in either of the four states are assumed to be Markovian, and independent of the exposed and infectious periods. These periods have general distributions, and are not affected by the possible migrations of the individuals. The infection “from distance” aspect introduces a new formulation of the infection process, which, together with the migration processes, brings technical challenges in proving the functional limit theorems. Generalizing the methods in Pang and Pardoux [<i>Ann. Appl. Probab.<i/> <b>32<b/> (2022) 1615–1665], we establish a functional law of large number (FLLN) and a function central limit theorem (FCLT) for the susceptible, exposed/latent, infectious and recovered processes. In the FLLN, the limit is determined by a set of Volterra integral equations. In the special case of deterministic exposed and infectious periods, the limit becomes a system of ODEs with delays. In the FCLT, the limit is given by a set of stochastic Volterra integral equations driven by a sum of independent Brownian motions and continuous Gaussian processes with an explicit covariance structure.en_US
dc.identifier.citationPang, Guodong and Pardoux, Étienne. "Multi-Patch Epidemic Models with General Exposed and Infectious Periods." <i>ESAIM: Probability and Statistics,</i> 27, (2023) EDP Sciences: 345-401. https://doi.org/10.1051/ps/2023003.en_US
dc.identifier.digitalps210058en_US
dc.identifier.doihttps://doi.org/10.1051/ps/2023003en_US
dc.identifier.urihttps://hdl.handle.net/1911/114537en_US
dc.language.isoengen_US
dc.publisherEDP Sciencesen_US
dc.rightsThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.en_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en_US
dc.titleMulti-Patch Epidemic Models with General Exposed and Infectious Periodsen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
ps210058.pdf
Size:
754.78 KB
Format:
Adobe Portable Document Format
Download
Collections
Faculty Publications
CMOR Publications