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)
A study of latency, reactivation and apoptosis throughout HIV pathogenesis. (English) Zbl 1205.92034
Summary: The capability of the HIV to persist latent inside CD4+ T-cells is currently regarded as a barrier to recovery from infection. On the other hand, immune activation, which is a normal immune reaction to pathogens, is now recognized as a key ingredient to sustaining the HIV caused infection. Further, it has been shown that activation of infected memory T-cells indirectly promotes apoptosis (programmed cell death) of bystander CD4+ and CD8+ T-cells. In this paper we use standard modeling techniques to develop a model compliant with the above mentioned mechanisms. Our farthest goal is to study how the long-term depletion of T-cells that characterizes HIV pathogenesis depends on these mechanisms. Consequently, we conduct parameter estimation, and apply standard results of sensitivity analysis and principal component analysis of the state variables with respect to the parameters.
MSC:
92C50Medical applications of mathematical biology
92C37Cell biology
34C60Qualitative investigation and simulation of models (ODE)
References:
[1]Nowak, M.; May, R.: Mathematical biology of HIV infections: antigenic variation and diversity threshold, Mathematical bioscience 106, No. 1, 1-21 (1991) · Zbl 0738.92008 · doi:10.1016/0025-5564(91)90037-J
[2]Kirschner, D.; Perelson, A.: A model for the immune system response to HIV: AZT treatment studies, Mathematical population dynamics: analysis of heterogeneity 1, 295-310 (1995)
[3]Perelson, A.; Nelson, P.: Mathematical analysis of HIV-1 dynamics in vivo, SIAM review 41, No. 1, 3-44 (1999) · Zbl 1078.92502 · doi:10.1137/S0036144598335107
[4]Perelson, A.: Modelling viral and immune system dynamics, Nature reviews immunology 2, No. 1, 28-36 (2002)
[5]Velasco-Hemandez, J.; Garcia, J.; Kirschner, D.: Remarks on modeling host–viral dynamics and treatment, Institute for mathematics and its applications 125, 287 (2002) · Zbl 1021.92017
[6]Callaway, D.; Perelson, A.: HIV-1 infection and low steady state viral loads, Bulletin of mathematical biology 64, No. 1, 29-64 (2002)
[7]Wodarz, D.; Nowak, M.: Mathematical models of HIV pathogenesis and treatment, Bioessays 24, No. 12, 1178-1187 (2002)
[8]Adams, B.; Banks, H.; Davidian, M.; Kwon, H.; Tran, H.; Wynne, S.; Rosenberg, E.: HIV dynamics: modeling, data analysis, and optimal treatment protocols, Journal of computational and applied mathematics 184, No. 1, 10-49 (2005) · Zbl 1075.92030 · doi:10.1016/j.cam.2005.02.004
[9]Regoes, R.; Yates, A.; Antia, R.: Mathematical models of cytotoxic T-lymphocyte Killing, Immunology and cell biology 85, No. 4, 274-279 (2007)
[10]Hadjiandreou, M.; Conejeros, R.; Vassiliadis, V.: Towards a long-term model construction for the dynamic simulation of HIV infection, Mathematical biosciences and engineering: MBE 4, No. 3, 489 (2007) · Zbl 1130.92038 · doi:10.3934/mbe.2007.4.489
[11]Stan, G.; Belmudes, F.; Fonteneau, R.; Zeggwagh, F.; Lefebvre, M.; Michelet, C.; Ernst, D.: Modelling the influence of activation-induced apoptosis of CD4 and CD8 T-cells on the immune system response of a HIV-infected patient, IET systems biology 2, No. 2, 94-102 (2008)
[12]Derdeyn, C.; Silvestri, G.: Viral and host factors in the pathogenesis of HIV infection, Current opinion in immunology 17, No. 4, 366-373 (2005)
[13]Grossman, Z.: What did mathematical models contribute to AIDS research?, Trends in ecology evolution 16, No. 8, 466-467 (2001)
[14]M. Hernández-Cedillo, Un modelo para la respuesta inmune a la infección con VIH, B.S. Thesis, Universidad Autónoma del Estado de Modelos, 2007.
[15]Vassena, L.; Proschan, M.; Fauci, A.; Lusso, P.: Interleukin 7 reduces the levels of spontaneous apoptosis in CD4+ and CD8+ T cells from HIV-1-infected individuals, Proceedings of the national Academy of sciences 104, No. 7, 2355 (2007)
[16]Mhawej, M.; Brunet-François, C.; Fonteneau, R.; Ernst, D.; Ferré, V.; Stan, G.; Raffi, F.; Moog, C.: Apoptosis characterizes immunological failure of HIV infected patients, Control engineering practice 17, No. 7, 798-804 (2009)
[17]Fauci, A.; Pantaleo, G.; Stanley, S.; Weissman, D.: Immunopathogenic mechanisms of HIV infection, (1996)
[18]Holm, G.; Gabuzda, D.: Distinct mechanisms of CD4+ and CD8+ T-cell activation and bystander apoptosis induced by human immunodeficiency virus type 1 virions, Journal of virology 79, No. 10, 6299 (2005)
[19]T. Kolda, R. Lewis, V. Torczon, Optimization by direct search: new perspectives on some classical and modern methods, Optimization 45(3) 385–482. · Zbl 1059.90146 · doi:10.1137/S0036144502428803