{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T18:46:03Z","timestamp":1776278763437,"version":"3.50.1"},"reference-count":30,"publisher":"Public Library of Science (PLoS)","issue":"4","license":[{"start":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T00:00:00Z","timestamp":1776211200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"\n In this work, we formulated a mathematical model on HIV\/AIDS transmission dynamics that incorporates the post-contact control measure. The six important compartments of the model are: Susceptible, under-3-day Exposed, Exposed-Uninfected, Treatment, Pre-AIDS, and AIDS. The next-generation operator approach was used to obtain the effective reproduction number\n \n \n \n \n \n \n (<\/mml:mo>\n \n \n R<\/mml:mi>\n <\/mml:mrow>\n \n e<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n . From the stability analysis, it was established that the disease-free equilibrium point of the model is locally asymptotically stable when the reproduction number is less than one\n \n \n \n \n \n (<\/mml:mo>\n \n \n R<\/mml:mi>\n <\/mml:mrow>\n \n e<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n <<\/mml:mo>\n 1<\/mml:mn>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n , and that it has a unique endemic equilibrium whenever this number exceeds unity. In the optimal control model, both Pre-contact Preventive and Anti-retroviral therapy (ART) control measures were incorporated. Pontryagin\u2019s maximum principle was used to form an optimal system. Seven control strategies were considered. The most cost-effective control measure was identified to be \u2018the optimal application of Pre-contact preventive control measures\u2019. In double control strategies, \u2018The combined use of Pre-contact Preventive and Anti-retroviral therapy\u2019 was also found to be better and most cost-effective than the other double control strategies in controlling the virus. The population dynamics of different classes with respect to the application of each of these strategies were simulated with MATLAB to assess the impact of these control measures on the control of the virus.\n <\/jats:p>","DOI":"10.1371\/journal.pone.0346773","type":"journal-article","created":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T17:51:30Z","timestamp":1776275490000},"page":"e0346773","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Mathematical Model on the optimal control of HIV\/AIDS transmission dynamics, incorporating the uninfected class after an effective exposure to the disease"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2710-9845","authenticated-orcid":true,"given":"Christopher Chukwuma","family":"Asogwa","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stephen Ekwueme","family":"Aniaku","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Obiageri Mary Joy","family":"Ezugorie","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Emmanuel","family":"Mbah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2026,4,15]]},"reference":[{"key":"pone.0346773.ref001","first-page":"575","article-title":"Global stability and optimal control of an HIV\/AIDS epidemic model with behavioral changes and treatment","volume":"29","author":"T Marsudi","year":"2021","journal-title":"Eng Lett"},{"key":"pone.0346773.ref002","doi-asserted-by":"crossref","first-page":"1","DOI":"10.5402\/2012\/215124","article-title":"Optimal control of a delayed HIV infection model with immune response using an efficient numerical method","volume":"2012","author":"K Hattaf","year":"2012","journal-title":"ISRN Biomath"},{"key":"pone.0346773.ref003","unstructured":"World Health Organization. HIV statistic, globally and by WHO region, 2023. Epidemiological fact sheet. Available from: https:\/\/www.who.int\/publications\/i\/item\/WHO-UCN-HHS-SIA-2023-0101"},{"key":"pone.0346773.ref004","unstructured":"World Health Organization. HIV and AIDS; 2025. Available from: https:\/\/www.who.int"},{"key":"pone.0346773.ref005","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.eclinm.2019.04.006","article-title":"Cost-effectiveness of HIV prevention interventions in sub-Saharan Africa: a systematic review","volume":"10","author":"S Sarkar","year":"2019","journal-title":"EClinicalMedicine"},{"issue":"1","key":"pone.0346773.ref006","doi-asserted-by":"crossref","DOI":"10.1101\/cshperspect.a006841","article-title":"Origins of HIV and the AIDS pandemic","volume":"1","author":"PM Sharp","year":"2011","journal-title":"Cold Spring Harb Perspect Med"},{"key":"pone.0346773.ref007","unstructured":"NIH. Understanding how HIV is transmitted; 2025. Available from; https:\/\/hivinfo.nih.gov\/understanding-hiv\/fact-sheets\/understanding-hiv-transmission"},{"issue":"9903","key":"pone.0346773.ref008","doi-asserted-by":"crossref","first-page":"1525","DOI":"10.1016\/S0140-6736(13)61809-7","article-title":"The end of AIDS: HIV infection as a chronic disease","volume":"382","author":"SG Deeks","year":"2013","journal-title":"Lancet"},{"key":"pone.0346773.ref009","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.ecocom.2016.12.001","article-title":"A SICA compartmental model in epidemiology with application to HIV\/AIDS in Cape Verde","volume":"30","author":"CJ Silva","year":"2017","journal-title":"Ecol Complex"},{"issue":"1","key":"pone.0346773.ref010","first-page":"93","article-title":"Global stability for a HIV\/AIDS model","volume":"67","author":"CJ Silva","year":"2017","journal-title":"Commun Fac Sci Univ Ank Ser"},{"key":"pone.0346773.ref011","author":"CDC","year":"2024"},{"key":"pone.0346773.ref012","article-title":"Antiretroviral post-exposure prophylaxis after sexual, injection-drug use, or other non-occupational exposure to HIV- CDC Recommendations and reports\/vol.74\/No 1 U.S. Department of Health and Human Services","author":"Center for Disease Control and Prevention","year":"2025","journal-title":"MMWR"},{"issue":"3","key":"pone.0346773.ref013","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1080\/17513750701775599","article-title":"Dynamical analysis of a multi-strain model of HIV in the presence of anti-retroviral drugs","volume":"2","author":"O Sharomi","year":"2008","journal-title":"J Biol Dyn"},{"key":"pone.0346773.ref014","article-title":"Modeling transmission dynamics of HIV\/AIDS: some results & challenges","author":"B Gumel Abba","year":"2007","journal-title":"DIMACS-SACEMA-AIMS Meeting; Stellenbosch, South Africa. Winnipeg, Manitoba, Canada: Department of Mathematics, University of Manitoba"},{"key":"pone.0346773.ref015","doi-asserted-by":"crossref","first-page":"4754426","DOI":"10.1155\/2023\/4754426","article-title":"Optimal control and bifurcation analysis of HIV model","volume":"2023","author":"KR Cheneke","year":"2023","journal-title":"Comput Math Methods Med"},{"key":"pone.0346773.ref016","author":"CDC","year":"2025"},{"key":"pone.0346773.ref017","author":"NIH","year":"2024"},{"key":"pone.0346773.ref018","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2021\/7471290","article-title":"Bifurcation and stability analysis of HIV transmission model with optimal control","volume":"2021","author":"KR Cheneke","year":"2021","journal-title":"J Math"},{"issue":"3","key":"pone.0346773.ref019","first-page":"288","article-title":"Reproduction numbers of infectious disease models","volume":"2","author":"P van den Driessche","year":"2017","journal-title":"Infect Dis Model"},{"issue":"1","key":"pone.0346773.ref020","first-page":"2722","article-title":"Stability and optimal control analysis of an SCIR epidemic model","volume":"2020","author":"O Peter","year":"2020","journal-title":"J Math Comput Sci"},{"key":"pone.0346773.ref021","doi-asserted-by":"crossref","DOI":"10.1016\/j.rinp.2021.104263","article-title":"Mathematical modeling of HIV\/AIDS with optimal control: a case study in Ethiopia","volume":"26","author":"TK Ayele","year":"2021","journal-title":"Results Phys"},{"key":"pone.0346773.ref022","first-page":"060033","article-title":"Optimal control and sensitivity analysis of HIV model with public health education campaign and antiretroviral therapy","author":"T Marsudi","year":"2018","journal-title":"AIP Conference Proceedings, vol. 2021"},{"key":"pone.0346773.ref023","author":"LS Pontryagin","year":"1987","journal-title":"Mathematical theory of optimal processes"},{"key":"pone.0346773.ref024","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-6380-7","volume-title":"Deterministic and stochastic optimal control, Vol. 1","author":"WH Fleming","year":"1975"},{"key":"pone.0346773.ref025","doi-asserted-by":"crossref","first-page":"831506","DOI":"10.1155\/2014\/831506","article-title":"Optimal control of HIV\/AIDS in the workplace in the presence of careless individuals","volume":"2014","author":"B Seidu","year":"2014","journal-title":"Comput Math Methods Med"},{"issue":"1","key":"pone.0346773.ref026","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.mbs.2010.10.007","article-title":"Epidemiological models with prevalence dependent endogenous self-protection measure","volume":"229","author":"SM Kassa","year":"2011","journal-title":"Math Biosci"},{"issue":"02","key":"pone.0346773.ref027","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1142\/S0218339010003329","article-title":"Analysis of an hiv\/aids model with public-health information campaigns and individual withdrawal","volume":"18","author":"F Nyabadza","year":"2010","journal-title":"J Biol Syst"},{"key":"pone.0346773.ref028","doi-asserted-by":"crossref","unstructured":"Campos C, Silva CJ, Torres DFM. Numerical optimal control of HIV transmission in Octave, MATLAB. 2019. https:\/\/doi.org\/10.3390\/mca25010001","DOI":"10.3390\/mca25010001"},{"key":"pone.0346773.ref029","first-page":"012035","article-title":"Mathematical model for HIV spread control program with ART treatment","volume":"974","author":"Maimunah","year":"2018","journal-title":"J Phys: Conf Ser"},{"issue":"3","key":"pone.0346773.ref030","doi-asserted-by":"crossref","first-page":"77","DOI":"10.5923\/j.am.20120203.06","article-title":"Mathematical modelling of HIV\/AIDS dynamics with treatment and vertical transmission","volume":"2","author":"AS Waziri","year":"2012","journal-title":"J Appl Math"}],"container-title":["PLOS One"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0346773","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T17:51:35Z","timestamp":1776275495000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0346773"}},"subtitle":[],"editor":[{"given":"Ali R.","family":"Ansari","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2026,4,15]]},"references-count":30,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2026,4,15]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pone.0346773","relation":{},"ISSN":["1932-6203"],"issn-type":[{"value":"1932-6203","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,15]]}}}