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Mathematical Biosciences and Engineering (MBE)
 

Immune response in virus model structured by cell infection-age
Pages: 887 - 909, Issue 5, October 2016

doi:10.3934/mbe.2016022      Abstract        References        Full text (1217.3K)           Related Articles

Cameron Browne - Mathematics Department, University of Louisiana at Lafayette, Lafayette, LA 70504, United States (email)

1 A. Akram and R. D. Inman, Immunodominance: A pivotal principle in host response to viral infections, Clinical Immunology, 143 (2012), 99-115.
2 C. L. Althaus and R. J. De Boer, Implications of ctl-mediated killing of hiv-infected cells during the non-productive stage of infection, PLoS One, 6 (2011), e16468-e16468.
3 C. L. Althaus, A. S. De Vos and R. J. De Boer, Reassessing the human immunodeficiency virus type 1 life cycle through age-structured modeling: life span of infected cells, viral generation time, and basic reproductive number, r0, Journal of Virology, 83 (2009), 7659-7667.
4 A. Balamurugan, A. Ali, J. Boucau, S. Le Gall, H. L. Ng and O. O. Yang, Hiv-1 gag cytotoxic t lymphocyte epitopes vary in presentation kinetics relative to hla class i downregulation, Journal of Virology, 87 (2013), 8726-8734.
5 H. T. Banks, D. M. Bortz and S. E. Holte, Incorporation of variability into the modeling of viral delays in hiv infection dynamics, Mathematical Biosciences, 183 (2003), 63-91.       
6 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.       
7 C. J. Browne and S. S. Pilyugin, Global analysis of age-structured within-host virus model, Discrete Contin. Dyn. Syst. Ser. B, 18 (2013), 1999-2017.       
8 R. W. Buckheit III, R. F. Siliciano and J. N. Blankson, Primary cd8+ t cells from elite suppressors effectively eliminate non-productively hiv-1 infected resting and activated cd4+ t cells, Retrovirology, 10 (2013), 1-12.
9 B. Buonomo and C. Vargas-De-León, Global stability for an hiv-1 infection model including an eclipse stage of infected cells, Journal of Mathematical Analysis and Applications, 385 (2012), 709-720.       
10 D. Y. Chen, A. Balamurugan, H. L. Ng, W. G. Cumberland and O. O. Yang, Epitope targeting and viral inoculum are determinants of nef-mediated immune evasion of hiv-1 from cytotoxic t lymphocytes, Blood, 120 (2012), 100-111.
11 R. V Culshaw and S. Ruan, A delay-differential equation model of hiv infection of cd4+ t-cells, Mathematical Biosciences, 165 (2000), 27-39.
12 R. J. De Boer, Which of our modeling predictions are robust, PLoS Comput. Biol., 8 (2012), e1002593, 5pp.       
13 R. D. Demasse and A. Ducrot, An age-structured within-host model for multistrain malaria infections, SIAM Journal on Applied Mathematics, 73 (2013), 572-593.       
14 A. Ducrot, Z. Liu and P. Magal, Essential growth rate for bounded linear perturbation of non-densely defined cauchy problems, Journal of Mathematical Analysis and applications, 341 (2008), 501-518.       
15 M. A. Gilchrist, D. Coombs and A. S. Perelson, Optimizing within-host viral fitness: Infected cell lifespan and virion production rate, Journal of Theoretical Biology, 229 (2004), 281-288.       
16 J. K. Hale and P. Waltman, Persistence in infinite-dimensional systems, SIAM Journal on Mathematical Analysis, 20 (1989), 388-395.       
17 G. Huang, X. Liu and Y. Takeuchi, Lyapunov functions and global stability for age-structured hiv infection model, SIAM Journal on Applied Mathematics, 72 (2012), 25-38.       
18 W. Kastenmuller, G. Gasteiger, J. H. Gronau, R. Baier, R. Ljapoci, D. H. Busch and I. Drexler, Cross-competition of cd8+ t cells shapes the immunodominance hierarchy during boost vaccination, The Journal of Experimental Medicine, 204 (2007), 2187-2198.
19 H. N. Kløverpris, R. P. Payne, J. B. Sacha, J. T. Rasaiyaah, F. Chen, M. Takiguchi, O. O. Yang, G. J. Towers, P. Goulder and J. G. Prado, Early antigen presentation of protective hiv-1 kf11gag and kk10gag epitopes from incoming viral particles facilitates rapid recognition of infected cells by specific cd8+ t cells, Journal of Virology, 87 (2013), 2628-2638.
20 X. Lai and X. Zou, Dynamics of evolutionary competition between budding and lytic viral release strategies, Mathematical Biosciences and Engineering: MBE, 11 (2014), 1091-1113.       
21 M. Y. Li and H. Shu, Global dynamics of an in-host viral model with intracellular delay, Bulletin of Mathematical Biology, 72 (2010), 1492-1505.       
22 P. Magal, C. C. McCluskey and G. F. Webb, Lyapunov functional and global asymptotic stability for an infection-age model, Applicable Analysis, 89 (2010), 1109-1140.       
23 P. Magal, Compact attractors for time periodic age-structured population models, Electronic Journal of Differential Equations, 2001 (2001), 1-35.       
24 P. Magal and X.-Q. Zhao, Global attractors and steady states for uniformly persistent dynamical systems, SIAM Journal on Mathematical Analysis, 37 (2005), 251-275.       
25 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.       
26 P. W. Nelson and A. S. Perelson, Mathematical analysis of delay differential equation models of hiv-1 infection, Mathematical Biosciences, 179 (2002), 73-94.       
27 M. A. Nowak and C. R. M. Bangham, Population dynamics of immune responses to persistent viruses, Science, 272 (1996), 74-79.
28 M. A. Nowak, R. M. May and K. Sigmund, Immune responses against multiple epitopes, Journal of Theoretical Biology, 175 (1995), 325-353.
29 R. P. Payne, H. Kløverpris, J. B. Sacha, Z. Brumme, C. Brumme, S. Buus, S. Sims, S. Hickling, L. Riddell, F. Chen, et al, Efficacious early antiviral activity of hiv gag-and pol-specific hla-b* 2705-restricted cd8+ t cells, Journal of Virology, 84 (2010), 10543-10557.
30 A. S. Perelson and P. W. Nelson, Mathematical analysis of hiv-1 dynamics in vivo, SIAM Review, 41 (1999), 3-44.       
31 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.
32 L. Rong, Z. Feng and A. S. Perelson, Mathematical analysis of age-structured hiv-1 dynamics with combination antiretroviral therapy, SIAM Journal on Applied Mathematics, 67 (2007), 731-756.       
33 L. Rong, M. A. Gilchrist, Z. Feng and A. S. Perelson, Modeling within-host hiv-1 dynamics and the evolution of drug resistance: Trade-offs between viral enzyme function and drug susceptibility, Journal of Theoretical Biology, 247 (2007), 804-818.       
34 J. B. Sacha, C. Chung, E. G. Rakasz, S. P. Spencer, A. K. Jonas, A. T. Bean, W. Lee, B. J. Burwitz, J. J. Stephany, J. T. Loffredo, et al, Gag-specific cd8+ t lymphocytes recognize infected cells before aids-virus integration and viral protein expression, The Journal of Immunology, 178 (2007), 2746-2754.
35 H. Shu, 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.       
36 H. Smith, An Introduction to Delay Differential Equations with Applications to the Life Sciences, volume 57. Springer Science & Business Media, 2011.       
37 H. L. Smith and P. De Leenheer, Virus dynamics: A global analysis, SIAM Journal on Applied Mathematics, 63 (2003), 1313-1327.       
38 X. Song, S. Wang and J. Dong, Stability properties and hopf bifurcation of a delayed viral infection model with lytic immune response, Journal of Mathematical Analysis and Applications, 373 (2011), 345-355.       
39 H. R. Thieme, Integrated semigroups and integrated solutions to abstract cauchy problems, Journal of Mathematical Analysis and Applications, 152 (1990), 416-447.       
40 H. R. Thieme, Quasi-compact semigroups via bounded perturbation, Advances in Mathematical Population Dynamics-Molecules, Cells and Man., Volume 6, Worlds Scientific, pages 691-711, 1997.       
41 H. R. Thieme et al, Semiflows generated by lipschitz perturbations of non-densely defined operators, Differential and Integral Equations, 3 (1990), 1035-1066.       
42 B. D. Walker and G. Y. Xu, Unravelling the mechanisms of durable control of hiv-1, Nature Reviews Immunology, 13 (2013), 487-498.
43 K. Wang, W. Wang, H. Pang and X. Liu, Complex dynamic behavior in a viral model with delayed immune response, Physica D: Nonlinear Phenomena, 226 (2007), 197-208.       
44 Y. Wang, Y. Zhou, F. Brauer and J. M. Heffernan, Viral dynamics model with ctl immune response incorporating antiretroviral therapy, Journal of Mathematical Biology, 67 (2013), 901-934.       
45 G. F. Webb, Theory of Nonlinear Age-Dependent Population Dynamics, CRC Press, 1985.       
46 D. Wodarz, Ecological and evolutionary principles in immunology, Ecology Letters, 9 (2006), 694-705.
47 S. Zhou, Z. Hu, W. Ma and F. Liao, Dynamics analysis of an hiv infection model including infected cells in an eclipse stage, Journal of Applied Mathematics, (2013), Art. ID 419593, 12 pp.       

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