Li, Qianqian; Cao, Shengshan; Chen, Xiao; Sun, Guiquan; Liu, Yunxi; Jia, Zhongwei Stability analysis of an HIV/AIDS dynamics model with drug resistance. (English) Zbl 1257.92034 Discrete Dyn. Nat. Soc. 2012, Article ID 162527, 13 p. (2012). Summary: A mathematical model of HIV/AIDS transmission incorporating treatment and drug resistance is built in this study. We firstly calculate the threshold value of the basic reproductive number \((R_0)\) by the next generation matrix and then analyze the stability of two equilibria by constructing a Lyapunov function. When \(R_0 < 1\), the system is globally asymptotically stable and converges to the disease-free equilibrium. Otherwise, the system has a unique endemic equilibrium which is also globally asymptotically stable. While an antiretroviral drug tries to reduce the infection rate and to prolong the patients’ survival, drug resistance is in fact neutralizing the effects of treatment. Cited in 2 Documents MSC: 92C60 Medical epidemiology 34K60 Qualitative investigation and simulation of models involving functional-differential equations 34K20 Stability theory of functional-differential equations PDF BibTeX XML Cite \textit{Q. Li} et al., Discrete Dyn. Nat. Soc. 2012, Article ID 162527, 13 p. (2012; Zbl 1257.92034) Full Text: DOI OpenURL References: [1] Journal of Acquired Immune Deficiency Syndromes 1 (3) pp 241– (1988) [2] DOI: 10.1093/imammb/3.4.229 [3] Nature 326 (6109) pp 137– (1987) [4] DOI: 10.1016/S0025-5564(02)00149-9 · Zbl 1008.92032 [5] DOI: 10.1016/j.nonrwa.2011.02.021 · Zbl 1225.34052 [6] Chinese Journal of Engineering Mathematics 27 (3) pp 534– (2010) [7] DOI: 10.1097/00002030-200107060-00014 [8] DOI: 10.1097/01.OLQ.0000112721.21285.A2 [9] DOI: 10.1016/j.crvi.2004.08.007 [10] DOI: 10.1126/science.287.5453.650 [11] DOI: 10.1080/17513750701775599 · Zbl 1154.92033 [12] Bulletin of the World Health Organization 80 (2) pp 89– (2002) [13] DOI: 10.1016/j.cam.2008.10.067 · Zbl 1162.92035 [14] Chinese Journal of Engineering Mathematics 26 (2) pp 226– (2009) [15] DOI: 10.1016/S0025-5564(02)00108-6 · Zbl 1015.92036 [16] The New England Journal of Medicine 365 (6) pp 493– (2011) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.