{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T18:28:01Z","timestamp":1780511281786,"version":"3.54.1"},"reference-count":22,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,3,11]],"date-time":"2020-03-11T00:00:00Z","timestamp":1583884800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"DST-FIST","award":["MSI-097 (only technical support to department)"],"award-info":[{"award-number":["MSI-097 (only technical support to department)"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>According to World Health Organization (WHO), the population suffering from human immunodeficiency virus (HIV) infection over a period of time may suffer from TB infection which increases the death rate. There is no cure for acquired immunodeficiency syndrome (AIDS) to date but antiretrovirals (ARVs) can slow down the progression of disease as well as prevent secondary infections or complications. This is considered as a medication in this paper. This scenario of HIV-TB co-infection is modeled using a system of non-linear differential equations. This model considers HIV-infected individual as the initial stage. Four equilibrium points are found. Reproduction number R0 is calculated. If R0 &gt;1 disease persists uniformly, with reference to the reproduction number, backward bifurcation is computed for pre-AIDS (latent) stage. Global stability is established for the equilibrium points where there is no Pre-AIDS TB class, point without co-infection and for the endemic point. Numerical simulation is carried out to validate the data. Sensitivity analysis is carried out to determine the importance of model parameters in the disease dynamics.<\/jats:p>","DOI":"10.3390\/axioms9010029","type":"journal-article","created":{"date-parts":[[2020,3,12]],"date-time":"2020-03-12T04:13:57Z","timestamp":1583986437000},"page":"29","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Dynamics of HIV-TB Co-Infection Model"],"prefix":"10.3390","volume":"9","author":[{"given":"Nita H","family":"Shah","sequence":"first","affiliation":[{"name":"Department of Mathematics, Gujarat University, Ahmedabad 380009, Gujarat, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nisha","family":"Sheoran","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Gujarat University, Ahmedabad 380009, Gujarat, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yash","family":"Shah","sequence":"additional","affiliation":[{"name":"GCS Medical College, Ahmedabad 380054, Gujarat, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,11]]},"reference":[{"key":"ref_1","unstructured":"(2020, January 03). Available online: https:\/\/www.who.int\/news-room\/fact-sheets\/detail\/hiv-aids."},{"key":"ref_2","unstructured":"(2020, January 03). Available online: https:\/\/www.who.int\/tb\/areas-of-work\/tb-hiv\/en\/."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1128\/CMR.00042-10","article-title":"HIV and tuberculosis: A deadly human syndemic","volume":"24","author":"Kwan","year":"2011","journal-title":"Clin. Microbiol. Rev."},{"key":"ref_4","unstructured":"(2020, January 03). Available online: https:\/\/www.avert.org\/professionals\/hiv-programming\/hiv-tb-coinfection."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1098\/rspa.1927.0118","article-title":"A contribution to the mathematical theory of epidemics","volume":"115","author":"Kermack","year":"1927","journal-title":"Proc. R. Soc. Lond. A Math. Phys. Char."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1339","DOI":"10.1016\/j.mcm.2007.07.005","article-title":"Qualitative analysis of second-order models of tumor\u2014Immune system competition","volume":"47","author":"Cattani","year":"2008","journal-title":"Math. Comput. Model."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1142\/S0218202507001875","article-title":"Hybrid two scales mathematical tools for active particles modelling complex systems with learning hiding dynamics","volume":"17","author":"Cattani","year":"2007","journal-title":"Math. Models Methods Appl. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1006\/tpbi.1998.1382","article-title":"Dynamics of Co-infection with M. tuberculosis and HIV-1","volume":"55","author":"Kirschner","year":"1999","journal-title":"Theor. Popul. Biol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"275","DOI":"10.3846\/13926292.2005.9637287","article-title":"Modelling and analysis of HIV-TB co-infection in a variable size population","volume":"10","author":"Naresh","year":"2005","journal-title":"Math. Model. Anal."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"6550","DOI":"10.1016\/j.apm.2016.01.054","article-title":"Modelling and stability of HIV\/AIDS epidemic model with treatment","volume":"40","author":"Huo","year":"2016","journal-title":"Appl. Math. Model."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1745","DOI":"10.1007\/s11538-009-9423-9","article-title":"Modeling HIV\/AIDS and tuberculosis coinfection","volume":"71","author":"Bhunu","year":"2009","journal-title":"Bull. Math. Biol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"815","DOI":"10.3934\/mbe.2009.6.815","article-title":"Modeling TB and HIV co-infections","volume":"6","author":"Roeger","year":"2009","journal-title":"Math. Biosci. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"222","DOI":"10.11648\/j.ajam.20160405.14","article-title":"Epidemic model of HIV\/AIDS transmission dynamics with different latent stages based on treatment","volume":"4","author":"Singh","year":"2016","journal-title":"Am. J. Appl. Math."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Silva, C.J., and Torres, D.F. (2014). Modeling TB-HIV syndemic and treatment. J. Appl. Math., 248407.","DOI":"10.1155\/2014\/248407"},{"key":"ref_15","unstructured":"(2020, January 03). Available online: https:\/\/aidsinfo.nih.gov\/understanding-hiv-aids\/fact-sheets\/26\/90\/hiv-and-tuberculosis--tb-."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1007\/BF00178324","article-title":"On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations","volume":"28","author":"Diekmann","year":"1990","journal-title":"J. Math. Biol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1007\/BF02218848","article-title":"Uniform persistence and flows near a closed positively invariant set","volume":"6","author":"Freedman","year":"1994","journal-title":"J. Dyn. Differ. Equ."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/0025-5564(92)90081-7","article-title":"Epidemic and demographic interaction in the spread of potentially fatal diseases in growing populations","volume":"111","author":"Thieme","year":"1992","journal-title":"Math. Biosci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1006\/tpbi.2000.1451","article-title":"A model for tuberculosis with exogenous reinfection","volume":"57","author":"Feng","year":"2000","journal-title":"Theor. Popul. Biol."},{"key":"ref_20","unstructured":"Castillo-Chavez, C., Blower, S., van den Driessche, P., Kirschner, D., and Yakubu, A.A. Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Dntroduction, Springer Science & Business Media."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"LaSalle, J.P. (1976). The stability of dynamical systems. Soc. Ind. Appl. Math., 25.","DOI":"10.21236\/ADA031020"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.12785\/amis\/080314","article-title":"Mathematical modeling towards the dynamical interaction of leptospirosis","volume":"8","author":"Khan","year":"2014","journal-title":"Appl. Math. Inf. Sci."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/9\/1\/29\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:06:11Z","timestamp":1760173571000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/9\/1\/29"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,11]]},"references-count":22,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,3]]}},"alternative-id":["axioms9010029"],"URL":"https:\/\/doi.org\/10.3390\/axioms9010029","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,11]]}}}