{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T14:54:52Z","timestamp":1787064892633,"version":"build-2736575974"},"reference-count":25,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"9","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["MBE"],"published-print":{"date-parts":[[2025]]},"DOI":"10.3934\/mbe.2025082","type":"journal-article","created":{"date-parts":[[2025,7,16]],"date-time":"2025-07-16T12:00:00Z","timestamp":1752667200000},"page":"2249-2268","source":"Crossref","is-referenced-by-count":1,"title":["Modeling the population dynamics of HIV\/AIDS with opportunistic infections at the severe stage of HIV"],"prefix":"10.3934","volume":"22","author":[{"given":"Mozart Umba","family":"Nsuami","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"name":"Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter Joseph","family":"Witbooi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2321","reference":[{"key":"key-10.3934\/mbe.2025082-1","unstructured":"<i>Statistics South Africa<\/i>, <i>Mid-year Population Estimates<\/i>, <i>Statistical Release P0302<\/i>, 2024. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.statssa.gov.za\/publications\/P0302\/P03022024.pdf\">https:\/\/www.statssa.gov.za\/publications\/P0302\/P03022024.pdf<\/ext-link>."},{"key":"key-10.3934\/mbe.2025082-2","doi-asserted-by":"publisher","unstructured":"T. B. Liu, D. S. Perlin, C. Xue, Molecular mechanisms of cryptococcal meningitis, <i>Virulence<\/i>, <b>3<\/b> (2012), 173\u2013181. https:\/\/doi.org\/10.4161\/viru.18685","DOI":"10.4161\/viru.18685"},{"key":"key-10.3934\/mbe.2025082-3","unstructured":"<i>National Institutes of Health and Others<\/i>, <i>HIV and Opportunistic Infections, Coinfections, and Conditions<\/i>, 2022. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/hivinfo.nih.gov\/understanding-hiv\/fact-sheets\/what-opportunistic-infection\">https:\/\/hivinfo.nih.gov\/understanding-hiv\/fact-sheets\/what-opportunistic-infection<\/ext-link>."},{"key":"key-10.3934\/mbe.2025082-4","doi-asserted-by":"publisher","unstructured":"J. Shaw, N. Matin, Opportunistic infections in HIV, <i>Medicine<\/i>, <b>50<\/b> (2022), 294\u2013297. https:\/\/doi.org\/10.1016\/j.mpmed.2022.02.010","DOI":"10.1016\/j.mpmed.2022.02.010"},{"key":"key-10.3934\/mbe.2025082-5","doi-asserted-by":"publisher","unstructured":"R. Rajasingham, N. P. Govender, A. Jordan, A. Loyse, A. Shroufi, D. W. Denning, et al., The global burden of HIV-associated cryptococcal infection in adults in 2020: A modelling analysis, <i>Lancet Infect. Dis.<\/i>, <b>22<\/b> (2022), 1748\u20131755. https:\/\/doi.org\/10.1016\/S1473-3099(22)00499-6","DOI":"10.1016\/S1473-3099(22)00499-6"},{"key":"key-10.3934\/mbe.2025082-6","doi-asserted-by":"publisher","unstructured":"N. A. Legare, V. C. Quan, N. P. Govender, J. W. Muchiri, Lived experience of people with cryptococcal meningitis: A qualitative study, <i>South. Afr. J. HIV Med.<\/i>, <b>25<\/b> (2024), 1560. https:\/\/doi.org\/10.4102\/sajhivmed.v25i1.1560","DOI":"10.4102\/sajhivmed.v25i1.1560"},{"key":"key-10.3934\/mbe.2025082-7","doi-asserted-by":"publisher","unstructured":"J. Rhein, K. H. Hullsiek, E. E. Evans, L. Tugume, E. Nuwagira, K. Ssebambulidde, et al., Detrimental outcomes of unmasking cryptococcal meningitis with recent ART initiation, <i>Open Forum Infect. Dis.<\/i>, <b>25<\/b> (2018), ofy122. https:\/\/doi.org\/10.1093\/ofid\/ofy122","DOI":"10.1093\/ofid\/ofy122"},{"key":"key-10.3934\/mbe.2025082-8","doi-asserted-by":"publisher","unstructured":"C. L. Wang, S. Gao, X. Z. Li, M. Martcheva, Modeling syphilis and HIV coinfection: a case study in the USA, <i>Bull. Math. Biol.<\/i>, <b>85<\/b> (2023), 20. https:\/\/doi.org\/10.1007\/s11538-023-01123-w","DOI":"10.1007\/s11538-023-01123-w"},{"key":"key-10.3934\/mbe.2025082-9","doi-asserted-by":"publisher","unstructured":"M. Byamukama, M. Karuhanga, D. Kajunguri, Mathematical analysis of the role of treatment and vaccination in the management of the HIV\/AIDS and pneumococcal pneumonia co\u2010infection, <i>J. Math.<\/i>, <b>1<\/b> (2025), 5879698. https:\/\/doi.org\/10.1155\/jom\/5879698","DOI":"10.1155\/jom\/5879698"},{"key":"key-10.3934\/mbe.2025082-10","doi-asserted-by":"publisher","unstructured":"E. Britz, O. Perovic, C. von Mollendorf, A. von Gottberg, S. Iyaloo, V. Quan, et al., The epidemiology of meningitis among adults in a South African province with a high HIV prevalence, 2009\u20132012, <i>PLoS One<\/i>, <b>11<\/b> (2016), e0163036. https:\/\/doi.org\/10.1371\/journal.pone.0163036","DOI":"10.1371\/journal.pone.0163036"},{"key":"key-10.3934\/mbe.2025082-11","doi-asserted-by":"publisher","unstructured":"N. P. Govender, G. Meintjes, P. Mangena, J. Nel, S. Potgieter, D. Reddy, et al., Southern African HIV Clinicians Society guideline for the prevention, diagnosis and management of cryptococcal disease among HIV-infected persons: 2019 update, <i>South. Afr. J. HIV Med.<\/i>, <b>20<\/b> (2019), 1\u201316. https:\/\/doi.org\/10.4102\/sajhivmed.v20i1.1030","DOI":"10.4102\/sajhivmed.v20i1.1030"},{"key":"key-10.3934\/mbe.2025082-12","doi-asserted-by":"publisher","unstructured":"G. J. Abiodun, N. Marcus, K. O. Okosun, P. J. Witbooi, A model for control of HIV\/AIDS with parental care, <i>Int. J. Biomath.<\/i>, <b>6<\/b> (2013), 1350006. https:\/\/doi.org\/10.1142\/S179352451350006X","DOI":"10.1142\/S179352451350006X"},{"key":"key-10.3934\/mbe.2025082-13","doi-asserted-by":"crossref","unstructured":"J. A. C. Hontelez, H. Goymann, Y. Berhane, P. Bhattacharjee, J. Bor, S. T. Chabata, et al., The impact of the PEPFAR funding freeze on HIV deaths and infections: a mathematical modelling study of seven countries in sub-Saharan Africa, <i>eClinicalMedicine<\/i>, <b>83<\/b> (2025). <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/doi.org\/10.1016\/j.eclinm.2025.103233\">https:\/\/doi.org\/10.1016\/j.eclinm.2025.103233<\/ext-link>","DOI":"10.1016\/j.eclinm.2025.103233"},{"key":"key-10.3934\/mbe.2025082-14","doi-asserted-by":"publisher","unstructured":"O. J. Peter, A. Yusuf, M. M. Ojo, S. Kumar, N. Kumari, F. A. Oguntolu, A mathematical model analysis of meningitis with treatment and vaccination in fractional derivatives, <i>Int. J. Appl. Comput. Math.<\/i>, <b>8<\/b> (2022), 117. https:\/\/doi.org\/10.1007\/s40819-022-01317-1","DOI":"10.1007\/s40819-022-01317-1"},{"key":"key-10.3934\/mbe.2025082-15","doi-asserted-by":"publisher","unstructured":"M. Fung, J. M. Babik, COVID-19 in immunocompromised hosts: what we know so far, <i>Clin. Infect. Dis.<\/i>, <b>72<\/b> (2021), 340\u2013350. https:\/\/doi.org\/10.1093\/cid\/ciaa863","DOI":"10.1093\/cid\/ciaa863"},{"key":"key-10.3934\/mbe.2025082-16","doi-asserted-by":"crossref","unstructured":"<i>Western Cape Department of Health in Collaboration with the National Institute for Communicable Diseases, South Africa<\/i>, Risk factors for coronavirus disease 2019 (COVID-19) death in a population cohort study from the Western Cape Province, South Africa, <i>Clin. Infect. Dis.<\/i>, <b>73<\/b> (2020), e2005\u2013e2015. <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/doi.org\/10.1093\/cid\/ciaa1198\">https:\/\/doi.org\/10.1093\/cid\/ciaa1198<\/ext-link>","DOI":"10.1093\/cid\/ciaa1198"},{"key":"key-10.3934\/mbe.2025082-17","doi-asserted-by":"publisher","unstructured":"A. A. Khan, R. Amin, S. Ullah, W. Sumelka, M. Altanji, Numerical simulation of a Caputo fractional epidemic model for the novel coronavirus with the impact of environmental transmission, <i>Alexandria Eng. J.<\/i>, <b>61<\/b> (2022), 5083\u20135095. https:\/\/doi.org\/10.1016\/j.aej.2021.10.008","DOI":"10.1016\/j.aej.2021.10.008"},{"key":"key-10.3934\/mbe.2025082-18","doi-asserted-by":"publisher","unstructured":"M. S. Abdo, K. Shah, H. A. Wahash, S. K. Panchal, On a comprehensive model of the novel coronavirus (COVID-19) under Mittag-Leffler derivative, <i>Chaos, Solitons Fractals<\/i>, <b>135<\/b> (2020), 109867. https:\/\/doi.org\/10.1016\/j.chaos.2020.109867","DOI":"10.1016\/j.chaos.2020.109867"},{"key":"key-10.3934\/mbe.2025082-19","doi-asserted-by":"publisher","unstructured":"N. Raza, S. Irum, S. Niazai, M. A. Ullah, M. Y. Alshahrani, A. Omame, A mathematical framework of HIV and TB co-infection dynamics, <i>Sci. Rep.<\/i>, <b>15<\/b> (2025), 11465. https:\/\/doi.org\/10.1038\/s41598-025-91871-7","DOI":"10.1038\/s41598-025-91871-7"},{"key":"key-10.3934\/mbe.2025082-20","doi-asserted-by":"publisher","unstructured":"S. Ullah, M. Altanji, M. A. Khan, A. Alshaheri, W. Sumelka, The dynamics of HIV\/AIDS model with fractal-fractional Caputo derivative, <i>Fractals<\/i>, <b>31<\/b> (2023), 2340015. https:\/\/doi.org\/10.1142\/S0218348X23400157","DOI":"10.1142\/S0218348X23400157"},{"key":"key-10.3934\/mbe.2025082-21","doi-asserted-by":"publisher","unstructured":"M. U. Nsuami, P. J. Witbooi, A model of HIV\/AIDS population dynamics including ARV treatment and pre-exposure prophylaxis, <i>Adv. Differ. Equations<\/i>, <b>2018<\/b> (2018), 1\u201312. https:\/\/doi.org\/10.1186\/s13662-017-1458-x","DOI":"10.1186\/s13662-017-1458-x"},{"key":"key-10.3934\/mbe.2025082-22","doi-asserted-by":"publisher","unstructured":"F. Nyabadza, Z. Mukandavire, S. D. Hove-Musekwa, Modelling the HIV\/AIDS epidemic trends in South Africa: Insights from a simple mathematical model, <i>Nonlinear Anal. Real World Appl.<\/i>, <b>12<\/b> (2011), 2091\u20132104. https:\/\/doi.org\/10.1016\/j.nonrwa.2010.12.024","DOI":"10.1016\/j.nonrwa.2010.12.024"},{"key":"key-10.3934\/mbe.2025082-23","doi-asserted-by":"publisher","unstructured":"F. Nyabadza, Z. Mukandavire, Modelling HIV\/AIDS in the presence of an HIV testing and screening campaign, <i>J. Theor. Biol.<\/i>, <b>280<\/b> (2011), 167\u2013179. https:\/\/doi.org\/10.1016\/j.jtbi.2011.04.021","DOI":"10.1016\/j.jtbi.2011.04.021"},{"key":"key-10.3934\/mbe.2025082-24","doi-asserted-by":"publisher","unstructured":"P. van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, <i>Math. Biosci.<\/i>, <b>180<\/b> (2002), 29\u201348. https:\/\/doi.org\/10.1016\/s0025-5564(02)00108-6","DOI":"10.1016\/s0025-5564(02)00108-6"},{"key":"key-10.3934\/mbe.2025082-25","doi-asserted-by":"publisher","unstructured":"S. Chibaya, F. Nyabadza, Mathematical modelling of the potential role of supplementary feeding for people living with HIV\/AIDS, <i>Int. J. Appl. Comput. Math.<\/i>, <b>5<\/b> (2019), 1\u201320. https:\/\/doi.org\/10.1007\/s40819-019-0660-9","DOI":"10.1007\/s40819-019-0660-9"}],"container-title":["Mathematical Biosciences and Engineering"],"original-title":[],"link":[{"URL":"http:\/\/www.aimspress.com\/article\/doi\/10.3934\/mbe.2025082?viewType=html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,16]],"date-time":"2025-07-16T12:00:02Z","timestamp":1752667202000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.aimspress.com\/article\/doi\/10.3934\/mbe.2025082"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"references-count":25,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2025]]}},"URL":"https:\/\/doi.org\/10.3934\/mbe.2025082","relation":{},"ISSN":["1551-0018"],"issn-type":[{"value":"1551-0018","type":"print"}],"subject":[],"published":{"date-parts":[[2025]]}}}