{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T07:33:36Z","timestamp":1778830416697,"version":"3.51.4"},"reference-count":58,"publisher":"Wiley","license":[{"start":{"date-parts":[[2022,2,13]],"date-time":"2022-02-13T00:00:00Z","timestamp":1644710400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational and Mathematical Methods"],"published-print":{"date-parts":[[2022,2,13]]},"abstract":"<jats:p>A mathematical model to describe the dynamic of a multiserotype infectious disease at the population level is studied. Applied to dengue fever epidemiology, we analyse a mathematical model with time delay to describe the cross-immunity protection period, including a key parameter for the antibody-dependent enhancement (ADE) effect, the well-known features of dengue fever infection. Numerical experiments are performed to show the stability of the coexistence equilibrium, which is completely determined by the basic reproduction number and by the invasion reproduction number, as well as the bifurcation structures for different scenarios of dengue fever transmission in a population. The model shows a rich dynamical behavior, from fixed points and periodic oscillations up to chaotic behaviour with complex attractors.<\/jats:p>","DOI":"10.1155\/2022\/2074325","type":"journal-article","created":{"date-parts":[[2022,2,13]],"date-time":"2022-02-13T23:05:06Z","timestamp":1644793506000},"page":"1-22","source":"Crossref","is-referenced-by-count":3,"title":["Effect of General Cross-Immunity Protection and Antibody-Dependent Enhancement in Dengue Dynamics"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0707-9511","authenticated-orcid":true,"given":"Vanessa","family":"Steindorf","sequence":"first","affiliation":[{"name":"Basque Center for Applied Mathematics (BCAM), Bilbao, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5284-0613","authenticated-orcid":true,"given":"Sergio","family":"Oliva","sequence":"additional","affiliation":[{"name":"Institute of Mathematics and Statistic, University of S\u00e3o Paulo, S\u00e3o Paulo, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0052-5336","authenticated-orcid":true,"given":"Jianhong","family":"Wu","sequence":"additional","affiliation":[{"name":"Laboratory for Industrial and Applied Mathematics, Department of Mathematics & Statistics, York University, Toronto, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8354-9944","authenticated-orcid":true,"given":"Ma\u00edra","family":"Aguiar","sequence":"additional","affiliation":[{"name":"Basque Center for Applied Mathematics (BCAM), Bilbao, Spain"},{"name":"Dipartimento di Matematica, Universita degli Studi di Trento, Italy"},{"name":"Ikerbasque, Basque Foundation for Science, Bilbao, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1038\/nature12060"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1128\/CMR.11.3.480"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1038\/nrmicro2460"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1126\/science.1185181"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1038\/ni.3515"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/S0065-3527(03)60011-4"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1126\/science.aan6836"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1038\/nri3014"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1056\/NEJMoa1506223"},{"key":"10","author":"World Health Organization","year":"2021"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1056\/NEJMoa1903869"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/S0140-6736(20)30414-1"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/S1473-3099(16)30168-2"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pntd.0005179"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/S1473-3099(17)30752-1"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1093\/cid\/cix882"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.3390\/v3122374"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1080\/14760584.2017.1276831"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/S0140-6736(18)30865-1"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.3390\/vaccines8040674"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pntd.0009258"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0049085"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.96.2.790"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0602960103"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1080\/17513758.2013.772253"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.5614\/cbms.2017.1.1.1"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1038\/nrmicro3430"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2011.08.043"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1016\/j.ecocom.2012.09.001"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.3934\/mbe.2019215"},{"issue":"8","key":"31","doi-asserted-by":"crossref","first-page":"1405","DOI":"10.1080\/00207160.2015.1050961","article-title":"Understanding dengue fever dynamics: a study of seasonality in vector borne disease models","volume":"9","author":"F. Rocha","year":"2016","journal-title":"International Journal of Computer Mathematics"},{"key":"32","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2006.03.002"},{"key":"33","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0709029105"},{"key":"34","article-title":"A new chaotic attractor in a basic multi-strain epidemiological model with temporary cross-immunity","author":"M. Aguiar","year":"2007"},{"key":"35","doi-asserted-by":"publisher","DOI":"10.1051\/mmnp:2008070"},{"key":"36","doi-asserted-by":"publisher","DOI":"10.1051\/mmnp\/20127301"},{"key":"37","doi-asserted-by":"publisher","DOI":"10.1080\/00207160902783532"},{"key":"38","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2013.12.009"},{"key":"39","first-page":"507","article-title":"Some epidemiological models with delays","volume-title":"Differential Equations and Application to Biology and to Industry","author":"P. Van den Driessche","year":"1996"},{"issue":"1","key":"40","first-page":"99","article-title":"Global dynamics of a delayed diffusive two-strain disease model","volume":"8","author":"D. Chen","year":"2009","journal-title":"Differential Equations and Applications"},{"issue":"1","key":"41","doi-asserted-by":"crossref","first-page":"816","DOI":"10.1063\/1.3225441","article-title":"A delay differential equation model for dengue fever transmission in selected countries of South-East Asia","volume":"1148","author":"W. Sakdanupahp","year":"2009","journal-title":"AIP Conference Proceedings"},{"key":"42","first-page":"139","article-title":"The stability and Hopf bifurcation of the dengue fever model with time delay","volume":"37","author":"J. Guan","year":"2017","journal-title":"Italian Journal of Pure and Applied Mathematics"},{"key":"43","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0158813"},{"key":"44","doi-asserted-by":"publisher","DOI":"10.1002\/mma.4068"},{"key":"45","doi-asserted-by":"crossref","DOI":"10.1101\/2021.07.22.453430","article-title":"Cross immunity protection and antibody dependent enhancement: a distributed delay dynamic model","author":"V. Steindorf","year":"2021"},{"key":"46","doi-asserted-by":"publisher","DOI":"10.3390\/tropicalmed5020078"},{"key":"47","doi-asserted-by":"publisher","DOI":"10.1016\/j.heliyon.2020.e05345"},{"key":"48","doi-asserted-by":"publisher","DOI":"10.1016\/j.rinp.2021.104473"},{"key":"49","doi-asserted-by":"publisher","DOI":"10.3934\/mbe.2007.4.205"},{"key":"50","doi-asserted-by":"publisher","DOI":"10.1155\/2016\/1598932"},{"key":"51","volume-title":"Nonlinear Volterra Integral Equations","author":"R. K. Miller","year":"1971"},{"key":"52","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(78)90065-7"},{"key":"53","article-title":"Gerencia de Estudos e An\u00e1lises da Din\u00e3mica Demogr\u00e1fica","author":"IBGE\/DPE\/Coordena\u00e7\u00e3o de Popula\u00e7\u00e3o e Indicadores Sociais","year":"2018"},{"key":"54","author":"Pan American Health Organization","year":"2021"},{"key":"55","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2017.09.004"},{"key":"56","doi-asserted-by":"publisher","DOI":"10.1016\/S0035-9203(01)90184-1"},{"key":"57","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1314933111"},{"key":"58","doi-asserted-by":"publisher","DOI":"10.1098\/rstb.1999.0428"}],"container-title":["Computational and Mathematical Methods"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmm\/2022\/2074325.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmm\/2022\/2074325.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmm\/2022\/2074325.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,13]],"date-time":"2022-02-13T23:05:13Z","timestamp":1644793513000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/cmm\/2022\/2074325\/"}},"subtitle":[],"editor":[{"given":"Chunrui","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2022,2,13]]},"references-count":58,"alternative-id":["2074325","2074325"],"URL":"https:\/\/doi.org\/10.1155\/2022\/2074325","relation":{},"ISSN":["2577-7408"],"issn-type":[{"value":"2577-7408","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,13]]}}}