{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T18:43:38Z","timestamp":1772045018852,"version":"3.50.1"},"reference-count":15,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,7,29]],"date-time":"2024-07-29T00:00:00Z","timestamp":1722211200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Viruses"],"abstract":"<jats:p>An HFMD outbreak spread over the city of H\u1ea3i Ph\u00f2ng from summer 2011 to autumn 2012. This epidemic was chosen because it was the very first HFMD epidemic in North Vietnam, eliminating thus interferences with previous outbreaks. This epidemic displayed three separate waves. A complete dataset was collected for more than 9500 patients during this period, which enabled us to analyze this epidemic at different scales. Access to the healthcare system was crucial during this period, which was possible due to a reorganization of the system in February\u2013March 2012. An analysis at the commune level enabled us to track the epidemic along certain communication routes. The three-waves structure reveals a wide disparity at the district level. We developed a mathematical model showing high accuracy at the adjustment of data for both the total number of cases and for the number of cases per week. As a consequence, the model was able to accurately determine the dates of the beginning and end of each wave and to show that they overlapped. Using mathematical functions associated with this model, it was possible to calculate the probability for a patient to belong to a specific wave.<\/jats:p>","DOI":"10.3390\/v16081217","type":"journal-article","created":{"date-parts":[[2024,7,29]],"date-time":"2024-07-29T16:37:17Z","timestamp":1722271037000},"page":"1217","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Modeling the Dynamic of Multiwave Diseases: The Model of Hand, Foot and Mouth Disease"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5752-7343","authenticated-orcid":false,"given":"Patrice","family":"Ravel","sequence":"first","affiliation":[{"name":"Institut de Recherche en Canc\u00e9rologie de Montpellier (INSERM U1194), Universit\u00e9 de Montpellier, CEDEX 5, 34298 Montpellier, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6548-0530","authenticated-orcid":false,"given":"Nghia Ngu","family":"Duy","sequence":"additional","affiliation":[{"name":"National Institute of Hygiene and Epidemiology, Hanoi 11611, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guilhem","family":"Kister","sequence":"additional","affiliation":[{"name":"Faculty of Pharmacy, University of Montpellier, 15 Av Charles Flahault, CEDEX 5, 34093 Montpellier, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Le Thi Song","family":"Huong","sequence":"additional","affiliation":[{"name":"Hai Phong Preventive Medicine Center, Hai Phong City 180000, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7294-1975","authenticated-orcid":false,"given":"Ankit","family":"Dwivedi","sequence":"additional","affiliation":[{"name":"Institut de Recherche en Canc\u00e9rologie de Montpellier (INSERM U1194), Universit\u00e9 de Montpellier, CEDEX 5, 34298 Montpellier, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christian A.","family":"Devaux","sequence":"additional","affiliation":[{"name":"IHU M\u00e9diterran\u00e9e Infections, CEDEX 5, 13385 Marseille, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tran Nhu","family":"Duong","sequence":"additional","affiliation":[{"name":"National Institute of Hygiene and Epidemiology, Hanoi 11611, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nguyen Tran","family":"Hien","sequence":"additional","affiliation":[{"name":"National Institute of Hygiene and Epidemiology, Hanoi 11611, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Laurent","family":"Gavotte","sequence":"additional","affiliation":[{"name":"Espace-Dev, University of Montpellier, CEDEX 5, 34093 Montpellier, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1202-1162","authenticated-orcid":false,"given":"Emmanuel","family":"Cornillot","sequence":"additional","affiliation":[{"name":"Institut de Recherche en Canc\u00e9rologie de Montpellier (INSERM U1194), Universit\u00e9 de Montpellier, CEDEX 5, 34298 Montpellier, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roger","family":"Frutos","sequence":"additional","affiliation":[{"name":"Cirad, UMR 17, Intertryp, TA-A17\/G, Campus International de Baillarguet, CEDEX 5, 34398 Montpellier, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1733","DOI":"10.3201\/eid1311.070632","article-title":"Epidemiologic and Virologic Investigation of Hand, Foot, and Mouth Disease, Southern Vietnam, 2005","volume":"13","author":"Thao","year":"2007","journal-title":"Emerg. 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