{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T04:08:30Z","timestamp":1761970110474,"version":"build-2065373602"},"reference-count":21,"publisher":"World Scientific Pub Co Pte Ltd","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2012,9]]},"abstract":"<jats:p> In this paper, we study HIV mathematical models with treatments. Two models with RT inhibitor and HIV protease inhibitor are studied. Local and global analysis is carried out. By identifying a critical number [Formula: see text] for both treatments, we show that if the treatment is at least [Formula: see text] effective, then the uninfected steady state P<jats:sub>0<\/jats:sub> is the only equilibrium in the feasible region, and P<jats:sub>0<\/jats:sub> is globally asymptotically stable. Therefore, no HIV infection persists and infected T cells and HIV virus are cleared over time. However, if the treatment is not effective enough, i.e. less than [Formula: see text], then a unique infected steady state P* emerges in the interior of the feasible region. P<jats:sub>0<\/jats:sub> becomes unstable and the system is uniformly persistent. Therefore, HIV infection persists. In this case, the unique infected steady state can be either stable or unstable. We show that it is locally stable only for r (the proliferation rate of T cells) small or large and unstable for some intermediate values. Global stability result is established for small values of r. Numerical simulation shows that once P* becomes unstable, periodic solution appears. <\/jats:p>","DOI":"10.1142\/s0218127412502276","type":"journal-article","created":{"date-parts":[[2012,10,16]],"date-time":"2012-10-16T02:49:37Z","timestamp":1350355777000},"page":"1250227","source":"Crossref","is-referenced-by-count":2,"title":["GLOBAL DYNAMICAL ANALYSIS OF HIV MODELS WITH TREATMENTS"],"prefix":"10.1142","volume":"22","author":[{"given":"LIANCHENG","family":"WANG","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Kennesaw State University, 1000 Chastain Rd., Kennesaw, GA 30144, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,10,15]]},"reference":[{"volume-title":"The Qualitative Theory of Ordinary Differential Equations: An Introduction","year":"1989","author":"Brauer F.","key":"rf1"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1986-0822433-4"},{"volume-title":"Stability and Asymptotic Behavior of Differential Equations","year":"1995","author":"Coppel W. 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