{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T14:47:08Z","timestamp":1790952428498,"version":"4.1.0"},"reference-count":54,"publisher":"Public Library of Science (PLoS)","issue":"12","license":[{"start":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T00:00:00Z","timestamp":1735603200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia","award":["KFU242721"],"award-info":[{"award-number":["KFU242721"]}]},{"name":"NASA Oklahoma Established Program to Stimulate Competitive Research (EPSCoR) Infrastructure Development","award":["80NSSC24M0109"],"award-info":[{"award-number":["80NSSC24M0109"]}]}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS ONE"],"abstract":"In this manuscript, we present a novel mathematical model for understanding the dynamics of HIV\/AIDS and analyzing optimal control strategies. To capture the disease dynamics, we propose a new Caputo-Fabrizio fractional-order mathematical model denoted as SE<\/jats:italic>I<\/jats:italic><\/jats:sub>E<\/jats:italic>U<\/jats:italic><\/jats:sub>PIATR<\/jats:italic>, where the exposed class is subdivided into two categories: exposed-identified E<\/jats:italic>I<\/jats:italic><\/jats:sub> and exposed-unidentified E<\/jats:italic>U<\/jats:italic><\/jats:sub> individuals. Exposed-identified individuals become aware of the disease within three days, while exposed-unidentified individuals remain unaware for more than three days. Simultaneously, we introduce a treatment compartment with post-exposure prophylaxis (PEP), represented as P<\/jats:italic>, designed for individuals of the exposed identified class. These individuals initiate treatment upon identification and continue for 28 days, resulting in full recovery from HIV. Additionally, we categorize infectious individuals into two groups: under-treatment individuals, denoted as T<\/jats:italic>, and those with fully developed AIDS not receiving antiretroviral therapy (ART) treatment, denoted as A<\/jats:italic>. We establish that the proposed model has a unique, bounded, and positive solution, along with other fundamental characteristics. Disease-free and endemic equilibrium points and their associated properties (such as the reproduction number R<\/mml:mi> 0<\/mml:mn><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula> and stability analysis) are determined. Sensitivity analysis is performed to assess the impact of parameters on R<\/mml:mi> 0<\/mml:mn><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula> and hence on the disease dynamics. Finally, we formulate a fractional optimal control problem to examine strategies for minimizing HIV\/AIDS infection while keeping costs at a minimum. We adopt the use of condoms and changes in sexual habits as optimal controls. The numerical results are presented and discussed through graphs.<\/jats:p>","DOI":"10.1371\/journal.pone.0315850","type":"journal-article","created":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T18:32:18Z","timestamp":1735669938000},"page":"e0315850","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":11,"title":["Analyzing HIV\/AIDS dynamics with a novel Caputo-Fabrizio fractional order model and optimal control measures"],"prefix":"10.1371","volume":"19","author":[{"given":"Azhar Iqbal Kashif","family":"Butt","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6924-5220","authenticated-orcid":true,"given":"Muhammad","family":"Imran","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Komal","family":"Azeem","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tariq","family":"Ismaeel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9494-8833","authenticated-orcid":true,"given":"Brett Allen","family":"McKinney","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2024,12,31]]},"reference":[{"issue":"13","key":"pone.0315850.ref001","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1056\/NEJM199803263381301","article-title":"Declining morbidity and mortality among patients with advanced human immunodeficiency virus infection","volume":"338","author":"FJ Palella","year":"1998","journal-title":"New England Journal of Medicine"},{"issue":"4","key":"pone.0315850.ref002","doi-asserted-by":"crossref","first-page":"748","DOI":"10.1016\/j.jbi.2009.04.008","article-title":"Health GIS and HIV\/AIDS studies: Perspective and retrospective","volume":"42","author":"R Kandwal","year":"2009","journal-title":"Journal of biomedical informatics"},{"key":"pone.0315850.ref003","unstructured":"World Health Organization, 2021. 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