ORCID
a http://orcid.org/0000-0002-2873-698X
b http://orcid.org /0000-0002-0860-6555
REFERENCES
- Montagnier L Historical essay. A history of HIV discovery. Science.
2002; 298 :1727-1728.
- Kirschner D.Using mathematics to understand HIV immune dynamics AMS
Notices. 1996; 43 (2): 191-202.
- Nowak M, Bangham Ch. Population dynamics of immune responses to
persistent viruses. Science. 1996;272 :74-79.
- Nowak M, May R. Virus dynamics: Mathematical principals of immunology
and virology, Oxford university press, New York, USA . 2001.
- Perelson A S. Modelling viral and immune system dynamics. Nature
reviews immunology. 2002; 2: 28-36
http://dx.doi.org/10.1038/nri700 .
- Perelson A S, Kirschner D, DeBoer R. Dynamics of HIV infection of CD+T
cells. Mathematical Biosciences. 1993; 114: 81-125.
- Nguyen P K, Nag D, Wu J C. Methods to assess stem cell lineage, fate
and function, Advanced Drug Delivery Reviews. 2010; vol. 62, no. 12:
1175–1186.
- Alqudah. M. A, Kallel S, Zarea S. Stability of a modifed mathematical
model of AIDS epidemic can stem cells ofer a new hope of cure for
HIV1?” Life Science Journal. 2016; vol. 13, no. 11.
- Alqudah M A, Zarea S, Jallouli S K. Mathematical Modeling to Study
Multistage Stem Cell Transplantation in HIV-1 Patients, Discrete
Dynamics in Nature and Society. 2019; Article ID 6379142, 8 pages.
- Cowan R, Morris V B. Determination of proliferative parameters from
growth curves, Cell Proliferation. 1987; vol. 20, no. 2: 153–159.
- Jandl J H. Blood. Textbook of hematology, 2ndedition, Little, Brown and company, USA. 1996; ISBN 0-316-45731-0.
- Johnston M D, Edwards C M, Bodmer W F., Maini Ph K, Jonathan S Ch.
Examples of mathematical modeling, Cell Cycle. 2007; Vol. 6, Issue
17:2106-2112, 1 September.
- Loefer M, Wichmann H E.A comprehensive mathematical model of stem cell
proliferation which reproduces most of the published experimental
results, Cell Proliferation. 1980; vol. 13, no. 5: 543–561.
- Czochra A M, Stiehl T, Ho A D, Jager v, Wagner W. Modeling of
asymmetric cell division in hematopoietic stem cells—regulation of
self-renewal is essential for efficient repopulation, Stem Cells and
Development. 2009; vol. 18(3):377–386. doi:
10.1089/scd.2008.0143 .
- Stiehl T, Czochra A. M. Characterization of stem cells using
mathematical models of multistage cell lineages,” Mathematical and
Computer Modelling. 2011; vol. 53, no. 7-8, pp. 1505–1517.
- Pazdziorek P R. Mathematical model of stem cell differentiation and
tissue regeneration with stochastic noise, Bulletin of Mathematical
Biology.2014; vol. 76, no. 7:1642–1669.
- Seibert P.On stability relative to a set and to the whole space, Proc.
5th internat. Conf. on Nonlin. Oscillations;Kiev
Vol. II, Izdat. Inst. Mat. Akad. NauK, USSR. .1970 ;448-457.
- Seibert P, Suarez R. Global stabilization of a certain class of
nonlinear systems, Matematicas Ecuaciones Diferenciales y Geometria.
1989.
- Farina L, Rinaldi S. Positive linear systems, theory and applications.
John Wiley and Sons, 2000;
DOI:10.1002/9781118033029.
- Luenberger D G. Introduction to Dynamic Systems. Theory, Models and
Applications. John Wiley and Sons, New York. 1979.
- Alizon S, Magnus C. Modelling the Course of an HIV Infection: Insights
from Ecology and Evolution Viruses. 2012;4, 1984-2013;
doi:10.3390/v4101984.
- Stafford M A, Corey L A, Cao Y B, Darr E S, Hob D D. Modeling Plasma
Virus Concentration during Primary HIV Infection J. theor. Biol.
2000;203, 285}301.
- Dhar M, Samaddar S, Bhattacharya P, Upadhyay R K. Viral dynamic model
with cellular immune response: A case study of HIV-1 infected
humanized mice. 2019; .524:1-4.
- Buonomo B, Vargas, Leon De. Global stability for an HIV-1 infection
model including an eclipse stage of infected cells. J Math. Anal.
Appl. 2012; 385:709–720.
- Gentry. S. Mathematical modelling of mutation acquisition in
hierarchical tissues: Quantification of the cancer stem cell
hypothesis. PhD thesis. 2008.