{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T01:37:49Z","timestamp":1781487469336,"version":"3.54.1"},"reference-count":49,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2021,7,30]],"date-time":"2021-07-30T00:00:00Z","timestamp":1627603200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,7,30]],"date-time":"2021-07-30T00:00:00Z","timestamp":1627603200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001342","name":"Department of Science and Technology, Republic of South Africa","doi-asserted-by":"crossref","award":["48518"],"award-info":[{"award-number":["48518"]}],"id":[{"id":"10.13039\/501100001342","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Acta Biotheor"],"published-print":{"date-parts":[[2021,12]]},"DOI":"10.1007\/s10441-021-09421-3","type":"journal-article","created":{"date-parts":[[2021,7,30]],"date-time":"2021-07-30T22:03:04Z","timestamp":1627682584000},"page":"543-589","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Optimal Control Strategies and Sensitivity Analysis of an HIV\/AIDS-Resistant Model with Behavior Change"],"prefix":"10.1007","volume":"69","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2626-7921","authenticated-orcid":false,"given":"Musa","family":"Rabiu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert","family":"Willie","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nabendra","family":"Parumasur","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,7,30]]},"reference":[{"key":"9421_CR1","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1016\/j.mbs.2017.01.005","volume":"285","author":"K Afassinou","year":"2017","unstructured":"Afassinou K, Chirove F, Govinder KS (2017) Pre-exposure prophylaxis and antiretroviral treatment interventions with drug resistance. Math Biosci 285:92\u2013101","journal-title":"Math Biosci"},{"key":"9421_CR2","unstructured":"Altman, L. (2000). A new AIDS mystery: prostitutes who have remained immune. New York Times, 2(3), A17. Available on https:\/\/www.nytimes.com\/2000\/02\/03\/us\/a-new-aids-mystery-prostitutes-who-have-remained-immune.html"},{"issue":"1","key":"9421_CR3","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1186\/s13662-018-1486-1","volume":"2018","author":"AU Awan","year":"2018","unstructured":"Awan AU, Hussain T, Okosun KO, Ozair M (2018) Qualitative analysis and sensitivity based optimal control of pine wilt disease. Adv. Differ. Equ. 2018(1):27","journal-title":"Adv. Differ. Equ."},{"issue":"Supplement3","key":"9421_CR4","doi-asserted-by":"publisher","first-page":"S361","DOI":"10.1086\/655965","volume":"202","author":"M Biasin","year":"2010","unstructured":"Biasin M, Clerici M, Piacentini L (2010) Innate immunity in resistance to HIV infection. J. Infect. Dis. 202(Supplement3):S361\u2013S365","journal-title":"J. Infect. Dis."},{"key":"9421_CR5","unstructured":"Blackwell T (2012) Blackwell on health: montreal researchers discover why some prostitutes evade HIV. National Post. Retrieved 20 Jan 2015"},{"issue":"9513","key":"9421_CR6","doi-asserted-by":"publisher","first-page":"817","DOI":"10.1016\/S0140-6736(06)68337-2","volume":"367","author":"P Braitstein","year":"2006","unstructured":"Braitstein P, Brinkhof MW, Dabis F, Schechter M, Boulle A, Miotti, P. & Bangsberg, D. R. (2006) Mortality of HIV-1-infected patients in the first year of antiretroviral therapy: comparison between low-income and high-income countries. Lancet (Lond Engl) 367(9513):817","journal-title":"Lancet (Lond Engl)"},{"issue":"9639","key":"9421_CR7","doi-asserted-by":"publisher","first-page":"669","DOI":"10.1016\/S0140-6736(08)60886-7","volume":"372","author":"JT Coates","year":"2008","unstructured":"Coates JT, Richter L, Caceres C (2008) Behavioral strategies to reduce HIV transmission: how to make them work better. Lancet 372(9639):669\u2013684","journal-title":"Lancet"},{"issue":"2","key":"9421_CR8","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1016\/j.pop.2012.03.004","volume":"39","author":"MT Coleman","year":"2012","unstructured":"Coleman MT, Pasternak RH (2012) Effective strategies for behavior change primary care: clinics in office practice. Prim Care 39(2):281\u2013305","journal-title":"Prim Care"},{"key":"9421_CR9","volume-title":"Advanced engineering mathematics","author":"HK Dass","year":"2008","unstructured":"Dass HK (2008) Advanced engineering mathematics. S. Chand Publishing, Bengaluru"},{"key":"9421_CR10","doi-asserted-by":"crossref","unstructured":"Diekmann O, Heesterbeek P, Metz JA (1990) On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. J Math Biol 28(4):356\u2013382","DOI":"10.1007\/BF00178324"},{"key":"9421_CR11","doi-asserted-by":"publisher","first-page":"781","DOI":"10.1007\/s13160-020-00422-2","volume":"37","author":"PMT Djomegni","year":"2020","unstructured":"Djomegni PMT, Tekle A, Dawed MY (2020) Pre-exposure prophylaxis HIV\/AIDS mathematical model with non classical isolation. Jpn J Indust Appl Math 37:781\u2013801. https:\/\/doi.org\/10.1007\/s13160-020-00422-2","journal-title":"Jpn J Indust Appl Math"},{"issue":"2","key":"9421_CR12","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/S0163-4453(99)90071-3","volume":"38","author":"PJ Easterbrook","year":"1999","unstructured":"Easterbrook PJ (1999) Long-term non-progression in HIV infection: definitions and epidemiological issues. J Infect. 38(2):71\u201373","journal-title":"J Infect."},{"key":"9421_CR13","unstructured":"Mendus E, T Ring (2016) A genetic mutation that blocks HIV may hold the key to future treatment and, perhaps, a cure. Available on: https:\/\/www.hivplusmag.com\/research-breakthroughs\/2016\/3\/23\/anyone-immune-hiv"},{"key":"9421_CR14","volume-title":"Deterministic and stochastic optimal control","author":"WH Fleming","year":"2012","unstructured":"Fleming WH, Rishel RW (2012) Deterministic and stochastic optimal control, 1st edn. Springer Science & Business Media, New York","edition":"1"},{"key":"9421_CR15","unstructured":"Green J (2015) The man who was immune to AIDS. NYMag.com. Retrieved, 01\u201320. Available on https:\/\/nymag.com\/health\/bestdoctors\/2014\/steve-crohn-aids-2014-6\/"},{"key":"9421_CR16","doi-asserted-by":"crossref","unstructured":"Grobler L, Siegfried N, Visser ME, Mahlungulu SSN, Volmink J (2013) Nutritional interventions for reducing morbidity and mortality in people with HIV. Cochrane Database Syst Rev, 2:CD004536","DOI":"10.1002\/14651858.CD004536.pub3"},{"key":"9421_CR17","unstructured":"HIV\/AIDS and human rights\u2019, UNAIDS, (2018) Available on: http:\/\/www.unaids.org"},{"issue":"6","key":"9421_CR18","doi-asserted-by":"publisher","first-page":"3468","DOI":"10.1128\/AAC.02307-13","volume":"58","author":"K Jeremiah","year":"2014","unstructured":"Jeremiah K, Denti P, Chigutsa E, Faurholt-Jepsen D, PrayGod G, Range N, Changalucha J (2014) Nutritional supplementation increases rifampin exposure among tuberculosis patients coinfected with HIV. Antimicrob Agents Chemother 58(6):3468\u20133474","journal-title":"Antimicrob Agents Chemother"},{"issue":"1","key":"9421_CR19","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1186\/s13662-018-1494-1","volume":"2018","author":"J Jia","year":"2018","unstructured":"Jia J, Xiao J (2018) Stability analysis of a disease resistance SEIRS model with nonlinear incidence rate. Adv Differ Equ 2018(1):75","journal-title":"Adv Differ Equ"},{"issue":"2","key":"9421_CR20","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/j.joems.2015.02.003","volume":"24","author":"NH Khanh","year":"2016","unstructured":"Khanh NH (2016) Stability analysis of an influenza virus model with disease resistance. J Egypt Math Soc 24(2):193\u2013199","journal-title":"J Egypt Math Soc"},{"key":"9421_CR21","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1097\/QAI.0b013e3181b32baf","volume":"53","author":"JR Koethe","year":"2010","unstructured":"Koethe JR, Lukusa A, Giganti MJ, Chi BH, Nyirenda CK, Limbada MI et al (2010) Association between weight gain and clinical outcomes among malnourished adults initiating antiretroviral therapy in Lusaka. Zambia J Acquir Immune Defic Syndr 53:507\u201313","journal-title":"Zambia J Acquir Immune Defic Syndr"},{"key":"9421_CR22","doi-asserted-by":"publisher","DOI":"10.1201\/9781420011418","volume-title":"Optimal control applied to biological models","author":"S Lenhart","year":"2007","unstructured":"Lenhart S, Workman JT (2007) Optimal control applied to biological models. Chapman and Hall, London"},{"key":"9421_CR23","doi-asserted-by":"publisher","first-page":"e38443","DOI":"10.1371\/journal.pone.0038443","volume":"7","author":"MR Lamb","year":"2012","unstructured":"Lamb MR, El-Sadr WM, Geng E, Nash D (2012) Association of adherence support and outreach services with total attrition, loss to follow-up, and death among ART patients in sub-Saharan Africa. PLoS ONE 7:e38443","journal-title":"PLoS ONE"},{"key":"9421_CR24","unstructured":"List of countries by HIV\/AIDS adult prevalence rate. Available on: https:\/\/en.wikipedia.org\/wiki\/List of countries by HIV\/AIDS adult prevalence rate"},{"issue":"1","key":"9421_CR25","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/j.biosystems.2010.12.010","volume":"104","author":"OD Makinde","year":"2011","unstructured":"Makinde OD, Okosun KO (2011) Impact of chemo-therapy on optimal control of malaria disease with infected immigrants. BioSystems 104(1):32\u201341","journal-title":"BioSystems"},{"issue":"1","key":"9421_CR26","doi-asserted-by":"publisher","first-page":"87","DOI":"10.4236\/am.2017.81008","volume":"8","author":"M Mastahun","year":"2017","unstructured":"Mastahun M, Abdurahman X (2017) Optimal control of an HIV\/AIDS epidemic model with infective immigration and behavioral change. Appl Math 8(1):87\u2013106","journal-title":"Appl Math"},{"issue":"1","key":"9421_CR27","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/s11524-005-9003-8","volume":"83","author":"M Marmor","year":"2006","unstructured":"Marmor M, Hertzmark K, Thomas SM, Halkitis PN, Vogler M (2006) Resistance to HIV infection. J Urban Health 83(1):5\u201317","journal-title":"J Urban Health"},{"issue":"155","key":"9421_CR28","first-page":"7749","volume":"8","author":"M Marsudi","year":"2014","unstructured":"Marsudi M, Andari A (2014) Sensitivity analysis of effect of screening and HIV therapy on the dynamics of spread of HIV. Appl Math Sci 8(155):7749\u20137763","journal-title":"Appl Math Sci"},{"key":"9421_CR29","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1016\/j.apm.2019.04.040","volume":"75","author":"P Ngina","year":"2019","unstructured":"Ngina P, Mbogo RW, Luboobi LS (2019) HIV drug resistance: insights from mathematical modelling. Appl Math Modell 75:141\u2013161","journal-title":"Appl Math Modell"},{"issue":"6","key":"9421_CR30","doi-asserted-by":"publisher","first-page":"3802","DOI":"10.1016\/j.apm.2012.08.004","volume":"37","author":"KO Okosun","year":"2013","unstructured":"Okosun KO, Makinde OD, Takaidza I (2013) Impact of optimal control on the treatment of HIV\/AIDS and screening of unaware infectives. Appl Math Modell 37(6):3802\u20133820","journal-title":"Appl Math Modell"},{"issue":"2","key":"9421_CR31","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1016\/j.biosystems.2012.09.008","volume":"111","author":"KO Okosun","year":"2013","unstructured":"Okosun KO, Rachid O, Marcus N (2013) Optimal control strategies and cost-effectiveness analysis of a malaria model. BioSystems 111(2):83\u2013101","journal-title":"BioSystems"},{"key":"9421_CR32","doi-asserted-by":"publisher","first-page":"g3187","DOI":"10.1136\/bmj.g3187","volume":"348","author":"MF Olsen","year":"2014","unstructured":"Olsen MF, Abdissa A, K\u00e6stel P, Tesfaye M, Yilma D, Girma T, Zerfu D (2014) Effects of nutritional supplementation for HIV patients starting antiretroviral treatment: randomised controlled trial in Ethiopia. BMJ 348:g3187","journal-title":"BMJ"},{"issue":"4","key":"9421_CR33","doi-asserted-by":"publisher","first-page":"412","DOI":"10.1038\/nm0496-412","volume":"2","author":"WA Paxton","year":"1996","unstructured":"Paxton WA, Martin SR, Tse D, O\u2019Brien TR, Skurnick J, VanDevanter NL, Koup RA (1996) Relative resistance to HIV-1 infection of CD4 lymphocytes from persons who remain uninfected despite multiple high-risk sexual exposures. Nat Med 2(4):412","journal-title":"Nat Med"},{"issue":"6","key":"9421_CR34","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1080\/17441692.2011.584325","volume":"6","author":"AF Phillips","year":"2011","unstructured":"Phillips AF, Pirkle CM (2011) Moving beyond behavior: advancing HIV risk prevention epistemologies and interventions (A report on the state of the literature). Global Public Health 6(6):577\u2013592","journal-title":"Global Public Health"},{"key":"9421_CR35","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1111\/j.1365-2125.1984.tb02377.x","volume":"17","author":"K Polasa","year":"1984","unstructured":"Polasa K, Murthy KJ, Krishnaswamy K (1984) Rifampicin kinetics in undernutrition. Br J Clin Pharmacol 17:481\u2013484. https:\/\/doi.org\/10.1111\/j.1365-2125.1984.tb02377.x","journal-title":"Br J Clin Pharmacol"},{"key":"9421_CR36","unstructured":"Population, total-Sub-Saharan Africa (2018) Available on: https:\/\/data.worldbank.org\/indicator\/SP.POP.TOTL?locations=ZG"},{"key":"9421_CR37","doi-asserted-by":"publisher","first-page":"603","DOI":"10.1007\/s11587-020-00496-7","volume":"69","author":"M Rabiu","year":"2020","unstructured":"Rabiu M, Willie R, Parumasur N (2020) Mathematical analysis of a disease-resistant model with imperfect vaccine, quarantine and treatment. Ricerche Mat 69:603\u2013627. https:\/\/doi.org\/10.1007\/s11587-020-00496-7","journal-title":"Ricerche Mat"},{"key":"9421_CR38","first-page":"2006143","volume":"9","author":"M Rabiu","year":"2020","unstructured":"Rabiu M, Willie R, Parumasur N (2020) Analysis of a virus-resistant HIV-1 Model with behavioural change in non-progressors. Biomath J 9:2006143","journal-title":"Biomath J"},{"key":"9421_CR39","first-page":"363","volume":"33","author":"M Rabiu","year":"2016","unstructured":"Rabiu M, Akinyemi ST (2016) Global analysis of dengue fever in a variable population. J Niger Assoc Math Phys. 33:363\u2013376","journal-title":"J Niger Assoc Math Phys."},{"key":"9421_CR40","unstructured":"Report on the global AIDS pandemic, UNAIDS (2012) available on http:\/\/www.unaids.org"},{"issue":"6593","key":"9421_CR41","doi-asserted-by":"publisher","first-page":"722","DOI":"10.1038\/382722a0","volume":"382","author":"M Samson","year":"1996","unstructured":"Samson M, Libert F, Doranz BJ, Rucker J, Liesnard C, Farber CM, Muyldermans G (1996) Resistance to HIV-1 infection in Caucasian individuals bearing mutant alleles of the CCR-5 chemokine receptor gene. Nature 382(6593):722","journal-title":"Nature"},{"key":"9421_CR42","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1016\/S0140-6736(06)69157-5","volume":"368","author":"V Simon","year":"2006","unstructured":"Simon V, Ho DD, Abdool-Karim Q (2006) HIV\/AIDS epidemiology, pathogenesis, prevention, and treatment. Lancet 368:489\u2013504","journal-title":"Lancet"},{"issue":"7444","key":"9421_CR43","doi-asserted-by":"publisher","first-page":"891","DOI":"10.1136\/bmj.328.7444.891","volume":"328","author":"JD Shelton","year":"2004","unstructured":"Shelton JD, Halperin DT, Nantulya V, Potts M, Gayle HD, Holmes KK (2004) Partner reduction is crucial for balanced \u201cABC\u201d approach to HIV prevention. BMJ 328(7444):891\u2013893","journal-title":"BMJ"},{"key":"9421_CR44","unstructured":"Singh M (2015) In life, man immune to HIV helped scientists fight virus. NPR.org. Retrieved 01\u201320"},{"key":"9421_CR45","unstructured":"The South African mid-year population (2019) Available on:http:\/\/www.statssa.gov.za\/publications\/P0302\/P03022019.pdf"},{"issue":"1","key":"9421_CR48","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10441-010-9095-8","volume":"59","author":"JM Tchuenche","year":"2011","unstructured":"Tchuenche JM, Khamis SA, Agusto FB, Mpeshe SC (2011) Optimal control and sensitivity analysis of an influenza model with treatment and vaccination. Acta biotheoretica 59(1):1\u201328","journal-title":"Acta biotheoretica"},{"key":"9421_CR47","unstructured":"University of Minnesota (2014) Why some people may be immune to HIV-1: clues. ScienceDaily. ScienceDaily, 20 November 2014. www.sciencedaily.com\/releases\/2014\/11\/141120141750.htm"},{"key":"9421_CR49","unstructured":"UNAIDS, World AIDS day (2015). http:\/\/www.unaids.org\/en\/resources\/fact-sheet. Accessed on 25 May 2016"},{"issue":"1\u20132","key":"9421_CR50","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/S0025-5564(02)00108-6","volume":"180","author":"P Van den Driessche","year":"2002","unstructured":"Van den Driessche P, Watmough J (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180(1\u20132):29\u201348","journal-title":"Math Biosci"}],"container-title":["Acta Biotheoretica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10441-021-09421-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10441-021-09421-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10441-021-09421-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,9]],"date-time":"2025-04-09T09:10:15Z","timestamp":1744189815000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10441-021-09421-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,30]]},"references-count":49,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["9421"],"URL":"https:\/\/doi.org\/10.1007\/s10441-021-09421-3","relation":{},"ISSN":["0001-5342","1572-8358"],"issn-type":[{"value":"0001-5342","type":"print"},{"value":"1572-8358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,30]]},"assertion":[{"value":"17 February 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 July 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 July 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"No conflict of interest as far as this research is concerned.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}