|
R. Adams and J. Fournier, Sobolev spaces, "Second edition", Pure Appl. Math., 140, Elsevier/Academic Press, Amsterdam, 2003.
|
|
I. Rob De Boer
and A. S. Perelson
, Target cell limited and immune control models of HIV infection: A comparison, Journal of Theoretical Biology, 190 (1998)
, 201-214.
|
|
B. Brandenburg, L. Y. Lee, M. Lakadamyali, M. J. Rust, X. Zhuang and J. M. Hogle, Imaging poliovirus entry in live cells, PLoS Biology, 5 (2007), e183, http://doi.org/10.1371/journal.pbio.0050183.
|
|
C. J. Browne
, A multi-strain virus model with infected cell age structure: Application to HIV, Nonlinear Analysis: Real World Applications, 22 (2015)
, 354-372.
doi: 10.1016/j.nonrwa.2014.10.004.
|
|
C. J. Browne
, Immune response in virus model structured by cell infection-age, Mathematical Biosciences and Engineering, 13 (2016)
, 887-909.
doi: 10.3934/mbe.2016022.
|
|
C. J. Browne
and S. S. Pilyugin
, Global analysis of age-structured within-host virus model, DCDS-B, 18 (2013)
, 1999-2017.
doi: 10.3934/dcdsb.2013.18.1999.
|
|
R. V. Culshaw
and S. Ruan
, A delay-differential equation model of HIV infection of CD4+ T-cells, Math. Biosci., 165 (2000)
, 27-39.
doi: 10.1016/S0025-5564(00)00006-7.
|
|
P. De Leenheer
and H. L. Smith
, Virus dynamics: A global analysis, SIAM J. Appl. Math., 63 (2003)
, 1313-1327.
doi: 10.1137/S0036139902406905.
|
|
M. N. Dixit
and A. S. Perelson
, Multiplicity of human immunodeficiency virus infections in lymphoid tissue, Journal of Virology, 78 (2004)
, 8942-8945.
|
|
P. Dustin
and D. Wodarz
, Modeling multiple infection of cells by viruses: Challenges and insights, Mathematical biosciences, 264 (2015)
, 21-28.
doi: 10.1016/j.mbs.2015.03.001.
|
|
J. K. Hale
, J. P. Lasalle
and M. Slemrod
, Theory of a general class of dissipative processes, J. Math. Anal. Appl., 39 (1972)
, 177-191.
doi: 10.1016/0022-247X(72)90233-8.
|
|
J. K. Hale, Asymptotic Behavior of Dissipative Systems, Mathematics Surveys and Monographs, American Mathematical Society, Providence, RI, 1988.
|
|
J. K. Hale
and P. Waltman
, Persistence in infinite-dimensional systems, SIAM J. Math. Anal., 20 (1989)
, 388-395.
doi: 10.1137/0520025.
|
|
S. Hongying
, L. Wang
and J. Watmough
, Global stability of a nonlinear viral infection model with infinitely distributed intracellular delays and CTL immune responses, SIAM Journal on Applied Mathematics, 73 (2013)
, 1280-1302.
doi: 10.1137/120896463.
|
|
G. Huang
, X. Liu
and Y. Takeuchi
, Lyapunov functions and global stability for age-structured HIV infection model, SIAM J. Appl. Math., 72 (2012)
, 25-58.
doi: 10.1137/110826588.
|
|
L. Josefsson, M. S. King, B. Makitalo, J. Brännström, W. Shao, F. Maldarelli and M. F. Kearney et al. Majority of CD4+ T cells from peripheral blood of HIV-1 infected individuals contain only one HIV DNA molecule, Proceedings of the National Academy of Sciences, 108 (2011), 11199-11204.
|
|
D. Kirschner
and G. F. Webb
, A model for treatment strategy in the chemotherapy of AIDS, Bull. Math. Biol., 58 (1996)
, 367-390.
doi: 10.1007/BF02458312.
|
|
P. Magal
and X. Q. Zhao
, Global attractors and steady states for uniformly persistent dynamical systems, SIAM J. Math. Anal., 37 (2005)
, 251-275.
doi: 10.1137/S0036141003439173.
|
|
C. C. McCluskey
, Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classes, Math. Biosci. Eng, 9 (2012)
, 819-841.
doi: 10.3934/mbe.2012.9.819.
|
|
P. W. Nelson
, M. A. Gilchrist
, D. Coombs
, J. M. Hyman
and A. S. Perelson
, An age-structured model of HIV infection that allows for variations in the production rate of viral particles and the death rate of productively infected cells, Math. Biosci. Eng., 1 (2004)
, 267-288.
doi: 10.3934/mbe.2004.1.267.
|
|
M. A. Nowak and R. M. May, Virus dynamics: Mathematical Principles of Immunology and Virology, Oxford University Press, 2000.
|
|
A. S. Perelson
, A. U. Neumann
, M. Markowitz
, J. M. Leonard
and D. D. Ho
, HIV-1 dynamics in vivo: Virion clearance rate, infected cell life-span and viral generation time, Science, 271 (1996)
, 1582-1586.
doi: 10.1126/science.271.5255.1582.
|
|
A. S. Perelson
and P. W. Nelson
, Mathematical analysis of HIV-1 dynamics in vivo, SIAM Rev., 41 (1999)
, 3-44.
doi: 10.1137/S0036144598335107.
|
|
H. Pourbashash
, S. S. Pilyugin
, P. De Leenheer
and C. C. McCluskey
, Global analysis of within host virus models with cell-to-cell viral transmission, DCDS-B, 19 (2014)
, 3341-3357.
doi: 10.3934/dcdsb.2014.19.3341.
|
|
L. Rong
, Z. Feng
and A. S. Perelson
, Mathematical analysis of age-structured HIV-1 dynamics with combination antiretroviral therapy, SIAM. J. Appl. Math., 67 (2007)
, 731-756.
doi: 10.1137/060663945.
|
|
Libin Rong
and A. S. Perelson
, Modeling HIV persistence, the latent reservoir, and viral blips, Journal of Theoretical Biology, 260 (2009)
, 308-331.
doi: 10.1016/j.jtbi.2009.06.011.
|
|
M. A. Stafford
, L. Corey
, Y. Cao
, E. S. Daar
, D. D. Ho
and A. S. Perelson
, Modeling plasma virus concentration during primary HIV infection, J. Theor. Biol., 23 (2000)
, 285-301.
doi: 10.1006/jtbi.2000.1076.
|
|
R. V. Ursache
, Y. E. Thomassen
, G. Van Eikenhorst
, P. J. T. Verheijen
and W. A. M. Bakker
, Mathematical model of adherent Vero cell growth and poliovirus production in animal component free medium, Bioprocess Biosyst Eng., 38 (2015)
, 543-555.
doi: 10.1007/s00449-014-1294-2.
|
|
Y. Wang
, Viral dynamics model with CTL immune response incorporating antiretroviral therapy, Journal of Mathematical Biology, 67 (2013)
, 901-934.
doi: 10.1007/s00285-012-0580-3.
|
|
G. F. Webb
and C. J. Browne. A model of the Ebola epidemics in West Africa incorporating age of infection
, A model of the Ebola epidemics in West Africa incorporating age of infection, Journal of Biological Dynamics, 10 (2016)
, 18-30.
doi: 10.1080/17513758.2015.1090632.
|
|
Y. Yang
, S. Ruan
and D. Xiao
, Global stability of an age-structured virus dynamics model with Bedington-Deangelis infection function, Math. Biosci. Eng., 12 (2015)
, 859-877.
doi: 10.3934/mbe.2015.12.859.
|
|
J. A. Zack
, S. J. Arrigo
, S. R. Weitsman
, A. S. Go
, A. Haislip
and I. S. Chen
, HIV-1 entry into quiescent primary lymphocytes: Molecular analysis reveals a labile latent viralstructure, Cell, 61 (1990)
, 213-222.
doi: 10.1016/0092-8674(90)90802-L.
|