# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Role of $CD{4}^{+}$ T-cell proliferation in HIV infection under antiretroviral therapy. (English) Zbl 1275.92033
The authors study a mathematical model describing the interaction between HIV viruses and CD4+ T cells. Both RT and protease inhibitor treatments are incorporated in the model. They assume that the CD4+ T cells proliferate according to a saturation form which is different from the commonly used logistic proliferation form in the literature. Both local and global analyses are carried out. A backward bifurcation has been observed. The global stability of the unique infected equilibrium has been established by using a new criterion developed by M.Y. Li and J.S. Muldowney which has been successfully utilized by some researchers for some high dimensional systems.
##### MSC:
 92C50 Medical applications of mathematical biology 92C60 Medical epidemiology 34C60 Qualitative investigation and simulation of models (ODE) 37N25 Dynamical systems in biology 34C23 Bifurcation (ODE)
##### Keywords:
viral dynamics; within-host model; backward bifurcation