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We show that a reproduction number $ R_0 $ exists whose threshold value determines the stability of the disease-free equilibrium, alongside the existence of an endemic one. We deduced conditions on the model parameters and ensured the stability and uniqueness of the endemic equilibrium. The transport equation was studied, and we showed some numerical experiments. Our results suggest that disease awareness dynamics can have a major role in epidemiological outcomes: we showed that even for high $ R_0 $, the infection prevalence could be made as small as desired, as long as the awareness decay was small. On the other hand, numerical evidence suggested that the relation between epidemiological outcomes and awareness levels was not straightforward, in the sense that sustained high awareness may not always lead to better outcomes, as compared to time-limited awareness peaks in response to outbreaks.&lt;\/p&gt;&lt;\/abstract&gt;<\/jats:p>","DOI":"10.3934\/nhm.20240012","type":"journal-article","created":{"date-parts":[[2024,2,28]],"date-time":"2024-02-28T10:23:27Z","timestamp":1709115807000},"page":"262-290","source":"Crossref","is-referenced-by-count":0,"title":["Modeling disease awareness and variable susceptibility with a structured epidemic model"],"prefix":"10.3934","volume":"19","author":[{"given":"Paulo","family":"Amorim","sequence":"first","affiliation":[{"name":"Instituto de Matem\u00e1tica, Universidade Federal do Rio de Janeiro, Av. Athos da Silveira Ramos 149, CT - Bloco C, Cidade Universit\u00e1ria - Ilha do Fund\u00e3o, 21941-909 Rio de Janeiro, RJ - Brasil"},{"name":"Escola de Matem\u00e1tica Aplicada, FGV EMAp, Praia de Botafogo 190, Rio de Janeiro, 22250-900, Brazil"}]},{"given":"Alessandro","family":"Margheri","sequence":"additional","affiliation":[{"name":"Centro de Matem\u00e1tica, Aplica\u00e7\u00f5es Fundamentais e Investiga\u00e7\u00e3o Operacional, Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias, Universidade de Lisboa, Campo Grande, Edif\u00edcio C6, piso 2, 1749-016 Lisboa, Portugal"}]},{"given":"Carlota","family":"Rebelo","sequence":"additional","affiliation":[{"name":"Centro de Matem\u00e1tica Computacional e Estoc\u00e1stica, Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias, Universidade de Lisboa, Campo Grande, Edificio C6, piso 2, 1749-016, Lisboa, Portugal"}]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.20240012-1","doi-asserted-by":"publisher","unstructured":"G. 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