{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T03:11:49Z","timestamp":1790737909409,"version":"4.1.0"},"reference-count":61,"publisher":"Public Library of Science (PLoS)","issue":"5","license":[{"start":{"date-parts":[[2023,5,5]],"date-time":"2023-05-05T00:00:00Z","timestamp":1683244800000},"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":"<jats:p>HIV\/AIDS and COVID-19 co-infection is a common global health and socio-economic problem. In this paper, a mathematical model for the transmission dynamics of HIV\/AIDS and COVID-19 co-infection that incorporates protection and treatment for the infected (and infectious) groups is formulated and analyzed. Firstly, we proved the non-negativity and boundedness of the co-infection model solutions, analyzed the single infection models steady states, calculated the basic reproduction numbers using next generation matrix approach and then investigated the existence and local stabilities of equilibriums using Routh-Hurwiz stability criteria. Then using the Center Manifold criteria to investigate the proposed model exhibited the phenomenon of backward bifurcation whenever its effective reproduction number is less than unity. Secondly, we incorporate time dependent optimal control strategies, using Pontryagin\u2019s Maximum Principle to derive necessary conditions for the optimal control of the disease. Finally, we carried out numerical simulations for both the deterministic model and the model incorporating optimal controls and we found the results that the model solutions are converging to the model endemic equilibrium point whenever the model effective reproduction number is greater than unity, and also from numerical simulations of the optimal control problem applying the combinations of all the possible protection and treatment strategies together is the most effective strategy to drastically minimizing the transmission of the HIV\/AIDS and COVID-19 co-infection in the community under consideration of the study.<\/jats:p>","DOI":"10.1371\/journal.pone.0284759","type":"journal-article","created":{"date-parts":[[2023,5,5]],"date-time":"2023-05-05T13:28:38Z","timestamp":1683293318000},"page":"e0284759","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":46,"title":["Bifurcation and optimal control analysis of HIV\/AIDS and COVID-19 co-infection model with numerical simulation"],"prefix":"10.1371","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4879-0921","authenticated-orcid":true,"given":"Belela Samuel","family":"Kotola","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9073-6075","authenticated-orcid":true,"given":"Shewafera Wondimagegnhu","family":"Teklu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yohannes Fissha","family":"Abebaw","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2023,5,5]]},"reference":[{"key":"pone.0284759.ref001","doi-asserted-by":"crossref","first-page":"2979","DOI":"10.1016\/j.aej.2021.01.041","article-title":"An epidemic prediction from analysis of a combined HIV-COVID-19 co-infection model via ABC-fractional operator","volume":"603","author":"Idris Ahmed","year":"2021","journal-title":"Alexandria Engineering Journal"},{"key":"pone.0284759.ref002","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-7612-3","volume-title":"An introduction to mathematical epidemiology","author":"Maia Martcheva","year":"2015"},{"key":"pone.0284759.ref003","first-page":"140","article-title":"COVID-19 and syphilis Co-Dynamics Analysis using Mathematical Modelling Approach","volume":"8","author":"Shewafera Wondimagegnhu Teklu","journal-title":"Frontiers in Applied Mathematics and Statistics"},{"issue":"2020","key":"pone.0284759.ref004","first-page":"110138","article-title":"Stability analysis of a delayed HIV-TB co-infection model in resource limitation settings","volume":"140","author":"Rajiv Aggarwal","journal-title":"Chaos, Solitons & Fractals"},{"key":"pone.0284759.ref005","first-page":"1","article-title":"A fractional order HIV\/AIDS epidemic model with Mittag-Leffler kernel","volume":"20211","author":"Muhammad Aslam","year":"2021","journal-title":"Advances in Difference Equations"},{"key":"pone.0284759.ref006","doi-asserted-by":"crossref","first-page":"48","DOI":"10.3390\/pr6050048","article-title":"Optimal control strategy for TB-HIV\/AIDS Co-infection model in the presence of behaviour modification","volume":"65","author":"Temesgen Debas Awoke","year":"2018","journal-title":"Processes"},{"key":"pone.0284759.ref007","first-page":"1","article-title":"Mathematical models of HIV\/AIDS and drug addiction in prisons","volume":"1355","author":"Afshin Babaei","year":"2020","journal-title":"The European Physical Journal Plus"},{"key":"pone.0284759.ref008","article-title":"Stability of an HIV\/AIDS treatment model with different stages","volume":"2015","author":"Hai-Feng Huo","year":"2015","journal-title":"Discrete Dynamics in Nature and Society"},{"key":"pone.0284759.ref009","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1007\/s11538-017-0384-0","article-title":"Mathematical analysis of the transmission dynamics of HIV syphilis co-infection in the presence of treatment for syphilis","volume":"803","author":"A. 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