{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T17:01:36Z","timestamp":1761930096218,"version":"3.40.5"},"reference-count":17,"publisher":"Walter de Gruyter GmbH","issue":"3-4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,5,26]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We propose a non-integer order model for the dynamics of the coinfection of HIV and HSV-2. We calculate the reproduction number of the model and study the local stability of the disease-free equilibrium. Simulations of the model for the variation of epidemiologically relevant parameters and the order of the non-integer order derivative, <jats:italic>\u03b1<\/jats:italic>, reveal interesting dynamics. These results are discussed from an epidemiologically point of view.<\/jats:p>","DOI":"10.1515\/ijnsns-2019-0008","type":"journal-article","created":{"date-parts":[[2020,1,26]],"date-time":"2020-01-26T09:01:02Z","timestamp":1580029262000},"page":"291-302","source":"Crossref","is-referenced-by-count":5,"title":["Analysis of a Non-integer Order Model for the Coinfection of HIV and HSV-2"],"prefix":"10.1515","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0729-1133","authenticated-orcid":false,"given":"Carla M. A.","family":"Pinto","sequence":"first","affiliation":[{"name":"Instituto Superior de Engenharia do Porto and Centre for Mathematics University of Porto , Rua Dr Ant\u00f3nio Bernardino de Almeida, 431 , Porto 4249-015 , Portugal"}]},{"given":"Ana R. M.","family":"Carvalho","sequence":"additional","affiliation":[{"name":"Faculty of Sciences , University of Porto , Porto , Portugal"}]}],"member":"374","published-online":{"date-parts":[[2020,1,28]]},"reference":[{"key":"2021062110463604572_j_ijnsns-2019-0008_ref_001_w2aab3b7e1380b1b6b1ab2ab1Aa","unstructured":"WHO, http:\/\/www.who.int\/."},{"key":"2021062110463604572_j_ijnsns-2019-0008_ref_002_w2aab3b7e1380b1b6b1ab2ab2Aa","doi-asserted-by":"crossref","unstructured":"Z. Feng, Z. Qiu, Z. Sang, C. Lorenzo and J. Glasser, Modeling the synergy between HSV-2 and HIV and potential impact of HSV-2 therapy, Math. Biosci. 245 (2013), 171\u2013187.","DOI":"10.1016\/j.mbs.2013.07.003"},{"key":"2021062110463604572_j_ijnsns-2019-0008_ref_003_w2aab3b7e1380b1b6b1ab2ab3Aa","doi-asserted-by":"crossref","unstructured":"C. Alvey, Z. Feng and J. Glasser, A model for the coupled disease dynamics of HIV and HSV-2 with mixing among and between genders, Math. Biosci. 265 (2015), 82\u2013100.","DOI":"10.1016\/j.mbs.2015.04.009"},{"key":"2021062110463604572_j_ijnsns-2019-0008_ref_004_w2aab3b7e1380b1b6b1ab2ab4Aa","unstructured":"U. S. Basak, J. Nayeem and C. N. Podder, Mathematical study of HIV and HSV-2 co-infection, Am. J. Math. Stat. 5(1) (2015), 15\u201323."},{"key":"2021062110463604572_j_ijnsns-2019-0008_ref_005_w2aab3b7e1380b1b6b1ab2ab5Aa","doi-asserted-by":"crossref","unstructured":"B. Ross, A brief history and exposition of the fundamental theory of fractional calculus, Fractional Calculus and its Applications, Springer Lecture Notes in Mathematics 57 (1975), 1\u201336.","DOI":"10.1007\/BFb0067096"},{"key":"2021062110463604572_j_ijnsns-2019-0008_ref_006_w2aab3b7e1380b1b6b1ab2ab6Aa","doi-asserted-by":"crossref","unstructured":"H. A. A. El-Saka, The fractional-order SIS epidemic model with variable population size, J. Egypt. Math. Soc. 22 (2014), 50\u201354.","DOI":"10.1016\/j.joems.2013.06.006"},{"key":"2021062110463604572_j_ijnsns-2019-0008_ref_007_w2aab3b7e1380b1b6b1ab2ab7Aa","doi-asserted-by":"crossref","unstructured":"C. M. A. Pinto and A. R. M. Carvalho, New findings on the dynamics of HIV and TB coinfection models, Appl. Math. Comput. 242 (2014), 36\u201346.","DOI":"10.1016\/j.amc.2014.05.061"},{"key":"2021062110463604572_j_ijnsns-2019-0008_ref_008_w2aab3b7e1380b1b6b1ab2ab8Aa","doi-asserted-by":"crossref","unstructured":"C. M. A. Pinto and A. R. M. Carvalho, A latency fractional order model for HIV dynamics, J. Comput. Appl. Math. 312 (2017), 240\u2013256.","DOI":"10.1016\/j.cam.2016.05.019"},{"key":"2021062110463604572_j_ijnsns-2019-0008_ref_009_w2aab3b7e1380b1b6b1ab2ab9Aa","doi-asserted-by":"crossref","unstructured":"C. M. A. Pinto and A. R. M. Carvalho, The role of synaptic transmission in a HIV model with memor, Appl. Math. Comput. 292 (2017), 76\u201395.","DOI":"10.1016\/j.amc.2016.07.031"},{"key":"2021062110463604572_j_ijnsns-2019-0008_ref_010_w2aab3b7e1380b1b6b1ab2ac10Aa","doi-asserted-by":"crossref","unstructured":"Z. M. Odibat and N. T. Shawagfeh, Generalized Taylor\u2019s formula, Appl. Math. Comput. 186 (2007), 286\u2013293.","DOI":"10.1016\/j.amc.2006.07.102"},{"key":"2021062110463604572_j_ijnsns-2019-0008_ref_011_w2aab3b7e1380b1b6b1ab2ac11Aa","doi-asserted-by":"crossref","unstructured":"W. Lin, Global existence theory and chaos control of fractional differential equations, J. Math. Anal. Appl. 332 (2007), 709\u2013726.","DOI":"10.1016\/j.jmaa.2006.10.040"},{"key":"2021062110463604572_j_ijnsns-2019-0008_ref_012_w2aab3b7e1380b1b6b1ab2ac12Aa","doi-asserted-by":"crossref","unstructured":"P. Driessche and P. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002), 29\u201348.","DOI":"10.1016\/S0025-5564(02)00108-6"},{"key":"2021062110463604572_j_ijnsns-2019-0008_ref_013_w2aab3b7e1380b1b6b1ab2ac13Aa","unstructured":"D. Matignon, Stability results for fractional differential equations with applications to control processing, Proceedings of the Computational Engineering in Syatems and Application Multiconference; IMACS, IEEE-SMC: Lille, France, 1996; Volume 2, pp. 963\u2013968."},{"key":"2021062110463604572_j_ijnsns-2019-0008_ref_014_w2aab3b7e1380b1b6b1ab2ac14Aa","doi-asserted-by":"crossref","unstructured":"M. S. Tavazoei and M. Haeri, Chaotic attractors in incommensurate fractional order systems, Physica D 237 (2018), 2628\u20132637.","DOI":"10.1016\/j.physd.2008.03.037"},{"key":"2021062110463604572_j_ijnsns-2019-0008_ref_015_w2aab3b7e1380b1b6b1ab2ac15Aa","unstructured":"Chavez, C. Castillo, Z. Feng and W. Huang, On the computation of R0 and its role on global stability, Math. Approaches Emerg. Re-Emerg. Infect. Dis.: Introduction. The IMA Volumes in Mathematics and Its Applications. 125 (2002), 31\u201365."},{"key":"2021062110463604572_j_ijnsns-2019-0008_ref_016_w2aab3b7e1380b1b6b1ab2ac16Aa","doi-asserted-by":"crossref","unstructured":"N. Chitnis, J. M. Hyman and J. M. Cushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bullet. Math. Biol. 70 (2008), 1272\u20131296.","DOI":"10.1007\/s11538-008-9299-0"},{"key":"2021062110463604572_j_ijnsns-2019-0008_ref_017_w2aab3b7e1380b1b6b1ab2ac17Aa","unstructured":"K. Diethelm and A. D. Freed, The FracPECE subroutine for the numerical solution of differential equations of fractional order, Forschung und wissenschaftliches Rechnen. 1999 (1998), 57\u201371."}],"container-title":["International Journal of Nonlinear Sciences and Numerical Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/ijnsns\/21\/3-4\/article-p291.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/ijnsns-2019-0008\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/ijnsns-2019-0008\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,21]],"date-time":"2021-06-21T13:43:11Z","timestamp":1624282991000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/ijnsns-2019-0008\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,28]]},"references-count":17,"journal-issue":{"issue":"3-4","published-online":{"date-parts":[[2020,5,9]]},"published-print":{"date-parts":[[2020,5,26]]}},"alternative-id":["10.1515\/ijnsns-2019-0008"],"URL":"https:\/\/doi.org\/10.1515\/ijnsns-2019-0008","relation":{},"ISSN":["2191-0294","1565-1339"],"issn-type":[{"type":"electronic","value":"2191-0294"},{"type":"print","value":"1565-1339"}],"subject":[],"published":{"date-parts":[[2020,1,28]]}}}