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)
Global dynamics of an HIV infection model with two classes of target cells and distributed delays. (English) Zbl 1253.37082
Summary: We investigate the global dynamics of an HIV infection model with two classes of target cells and multiple distributed intracellular delays. The model is a 5-dimensional nonlinear delay ODE that describes the interaction of the HIV with two classes of target cells, CD4${}^{+}$ T cells and macrophages. The incidence rate of infection is given by saturation functional response. The model has two types of distributed time delays describing time needed for infection of target cell and virus replication. This model can be seen as a generalization of several models given in the literature describing the interaction of the HIV with one class of target cells, CD4${}^{+}$ T cells. Lyapunov functionals are constructed to establish the global asymptotic stability of the uninfected and infected steady states of the model. We have proven that if the basic reproduction number ${R}_{0}$ is less than unity then the uninfected steady state is globally asymptotically stable, and if ${R}_{0}>1$ then the infected steady state exists and it is globally asymptotically stable.
MSC:
 37N25 Dynamical systems in biology 92D30 Epidemiology 34K60 Qualitative investigation and simulation of models 34K25 Asymptotic theory of functional-differential equations