{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T04:50:12Z","timestamp":1777611012451,"version":"3.51.4"},"reference-count":24,"publisher":"Wiley","license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100004837","name":"Ministerio de Ciencia e Innovaci\u00f3n","doi-asserted-by":"publisher","award":["MTM2011-24321"],"award-info":[{"award-number":["MTM2011-24321"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004837","name":"Ministerio de Ciencia e Innovaci\u00f3n","doi-asserted-by":"publisher","award":["MTM2011-25238"],"award-info":[{"award-number":["MTM2011-25238"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004837","name":"Ministerio de Ciencia e Innovaci\u00f3n","doi-asserted-by":"publisher","award":["MTM2011-24321"],"award-info":[{"award-number":["MTM2011-24321"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004837","name":"Ministerio de Ciencia e Innovaci\u00f3n","doi-asserted-by":"publisher","award":["MTM2011-25238"],"award-info":[{"award-number":["MTM2011-25238"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Dipartimento di Matematica \u201cGiuseppe Peano\u201d","award":["MTM2011-24321"],"award-info":[{"award-number":["MTM2011-24321"]}]},{"name":"Dipartimento di Matematica \u201cGiuseppe Peano\u201d","award":["MTM2011-25238"],"award-info":[{"award-number":["MTM2011-25238"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2015]]},"abstract":"<jats:p>Traditional biomedical approaches treat diseases in isolation, but the importance of synergistic disease interactions is now recognized. As a first step we present and analyze a simple coinfection model for two diseases simultaneously affecting a population. The host population is affected by the<jats:italic>primary disease<\/jats:italic>, a long-term infection whose dynamics is described by a SIS model with demography, which facilitates individuals acquiring a second disease,<jats:italic>secondary<\/jats:italic>(<jats:italic>or opportunistic<\/jats:italic>)<jats:italic>disease<\/jats:italic>. The secondary disease is instead a short-term infection affecting only the primary infected individuals. Its dynamics is also represented by a SIS model with no demography. To distinguish between short- and long-term infection the complete model is written as a two-time-scale system. The primary disease acts at the slow time scale while the secondary disease does at the fast one, allowing a dimension reduction of the system and making its analysis tractable. We show that an opportunistic disease outbreak might change drastically the outcome of the primary epidemic process, although it does among the outcomes allowed by the primary disease. We have found situations in which either acting on the opportunistic disease transmission or recovery rates or controlling the susceptible and infected population size allows eradicating\/promoting disease endemicity.<\/jats:p>","DOI":"10.1155\/2015\/275485","type":"journal-article","created":{"date-parts":[[2015,4,21]],"date-time":"2015-04-21T17:07:45Z","timestamp":1429636065000},"page":"1-10","source":"Crossref","is-referenced-by-count":6,"title":["A Time Scales Approach to Coinfection by Opportunistic Diseases"],"prefix":"10.1155","volume":"2015","author":[{"given":"Marcos","family":"Marv\u00e1","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica y Matem\u00e1ticas, Universidad de Alcal\u00e1, 28871 Alcal\u00e1 de Henares, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7215-5114","authenticated-orcid":true,"given":"Ezio","family":"Venturino","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica \u201cGiuseppe Peano\u201d, Universit\u00e0 di Torino, Via Carlo Alberto 10, 10123 Torino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rafael","family":"Bravo de la Parra","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica y Matem\u00e1ticas, Universidad de Alcal\u00e1, 28871 Alcal\u00e1 de Henares, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"12","doi-asserted-by":"publisher","DOI":"10.1017\/s003118200001698x"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jinf.2011.06.005"},{"key":"23","year":"2009"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1128\/cmr.00042-10"},{"key":"27","year":"2011"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1126\/science.1132338"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pntd.0002380"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1002\/ajhb.20618"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.amepre.2010.12.010"},{"key":"5","year":"1996"},{"key":"26","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1177\/003591576505800521","volume":"58","year":"1965","journal-title":"Proceedings of the Royal Society of Medicine"},{"issue":"6","key":"19","first-page":"901","volume":"59","year":"1981","journal-title":"Bulletin of the World Health Organization"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1186\/1471-2334-13-112"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-78273-5_5"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.ecocom.2011.09.001"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/j.ecocom.2011.09.002"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3516-1"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2013.12.006"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/s0169-5347(01)02144-9"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1017\/s0950268802007148"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-78911-6_2"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pbio.0030262"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1016\/j.ecocom.2013.06.002"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1080\/00207160.2013.867955"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/275485.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/275485.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/275485.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,23]],"date-time":"2019-08-23T18:18:42Z","timestamp":1566584322000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2015\/275485\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"references-count":24,"alternative-id":["275485","275485"],"URL":"https:\/\/doi.org\/10.1155\/2015\/275485","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015]]}}}