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Here, in particular, we apply our general framework to the current COVID-19 pandemic. We establish, at a theoretical level, sufficient conditions which lead to particular solutions exhibiting irregular oscillations and interpret those particular solutions as pandemic waves. We perform numerical simulations of a set of relevant scenarios which show how the microscopic processes impact the macroscopic dynamics.<\/p><\/jats:p>","DOI":"10.3934\/nhm.2022010","type":"journal-article","created":{"date-parts":[[2022,3,26]],"date-time":"2022-03-26T14:17:26Z","timestamp":1648304246000},"page":"333","source":"Crossref","is-referenced-by-count":3,"title":["Mathematical analysis of a hybrid model: Impacts of individual behaviors on the spreading of an epidemic"],"prefix":"10.3934","volume":"17","author":[{"given":"Guillaume","family":"Cantin","sequence":"first","affiliation":[{"name":"Laboratoire des Sciences du Num\u00e9rique, LS2N UMR CNRS 6004, Universit\u00e9 de Nantes, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cristiana J.","family":"Silva","sequence":"additional","affiliation":[{"name":"Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arnaud","family":"Banos","sequence":"additional","affiliation":[{"name":"UMR IDEES, CNRS, 25 rue Philippe Lebon BP 1123, 76063 Le Havre Cedex, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.2022010-1","doi-asserted-by":"publisher","unstructured":"M. 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